# 2024

### Tightening the reins on non-minimal dark sector physics: Interacting Dark Energy with dynamical and non-dynamical equation of state

William Giarè, Yuejia Zhai, Supriya Pan, Eleonora Di Valentino, Rafael C. Nunes, Carsten van de Bruck[arXiv: 2404.02110] We offer a thorough review of Interacting Dark Energy (IDE) cosmology, which explores models involving a non-gravitational interplay between Dark Matter (DM) and Dark Energy (DE). We expand the dark sector physics by considering two scenarios: one with a constant DE equation of state and another with a dynamic equation of state given by a CPL parameterization. In both cases, we identify two distinct physical regimes based on whether the equation of state resembles phantom or quintessence behavior. We examine various IDE models in light of Cosmic Microwave Background data from the Planck satellite and the Atacama Cosmology Telescope, both independently and combined with data from Supernovae and Baryon Acoustic Oscillations. Our analysis refines previous studies, narrowing down the parameter space for these models and indicating challenges in resolving cosmological tensions solely within the IDE framework.

My Contribution: I implemented the dynamical Dark Energy Equation of State for IDE and developed a novel sampling methodology that allows us to explore the quintessence and phantom regimes in the dynamical case properly. I implemented the different updated likelihoods in cobaya (Pantheon-Plus and updated BAO). I performed the vast majority of the MCMC analyses, created all figures, and contributed to the paper writing.

### Testing scale-invariant inflation against cosmological data

Chiara Checchini, Mariaveronica De Angelis, William Giarè, Massimiliano Rinaldi, Sunny Vagnozzi[arXiv: 2403.04316] We investigate scale-invariant inflation, addressing the dynamics by solving the two-field trajectory to yield effective dynamics resembling that of a single field. This results in vanishing entropy perturbations and protects the model from destabilization effects. We establish stringent upper limits on the non-minimal coupling strength, excluding conformal coupling at a high significance level. We demonstrate the model's robustness against initial conditions. We argue that the model predicts a minimal level of primordial tensor modes, well within the detectable range of upcoming CMB experiments.

My Contribution: I contributed to the data analysis by applying the methodology that some of us developed in [arXiv:2306.12414]. I realized Fig.2, Fig.3, and Fig.4. I contributed to the paper writing.

### Gravitational waves in a cyclic Universe: resilience through cycles and vacuum state

Mariaveronica De Angelis, Adam Smith,William Giarè, Carsten van de Bruck[arXiv: 2403.00533] We generalize the calculation of the spectrum of gravitational waves in a cyclic Universe, making no assumptions about the vacuum state of the theory and including the contribution of tensor modes produced during the dark energy phase of the previous cycle. We show that these modes have minimal impact on the spectrum observed in the current cycle, while avoiding backreaction effects sets restrictive constraints on deviations away from the Bunch-Davies vacuum during this phase, limiting the overall freedom to consider alternative vacua in the cyclic Universe.

My Contribution: I contributed to the calculation and the paper writing.

### Testing α-attractor quintessential inflation against CMB and low-redshift data

William Giarè, Eleonora Di Valentino,Eric V. Linder, Enrico Specogna[arXiv: 2402.01560] We test α-attractor quintessential inflation in light of Cosmic Microwave Background measurements from the Planck satellite, the Atacama Cosmology Telescope, and B-mode polarization data from the BICEP/Keck collaboration – both alone and in combination with low-redshift observations. The model can provide equally good fits as ΛCDM for a broad range of parameter values.

My Contribution: I implemented the model and performed the MCMC analysis. I contributed to the paper writing.

# 2023

### A double take on early and interacting dark energy from JWST

Matteo Forconi, William Giarè, Olga Mena, Ruchika, Eleonora Di Valentino, Alessandro Melchiorri, Rafael C. Nunes[arXiv:2312.11074] We test alternative cosmological perturbation histories in light of the preliminary James Webb Space Telescope (JWST) data. We argue that models with a larger matter component and/or a larger scalar spectral index can substantially improve the fit to JWST measurements. In this regard, phenomenological extensions related to the dark energy sector of the theory are appealing alternatives, with Early Dark Energy emerging as an excellent candidate to explain (at least in part) the unexpected JWST preference for larger stellar mass densities.

My Contribution: I performed the MCMC analysis of Early Dark Energy and Interacting Dark Energy. I contributed to the JWST data-analysis and the paper writing.

### Measuring the reionization optical depth without large-scale CMB polarization

William Giarè, Eleonora Di Valentino, Alessandro Melchiorri[arXiv:2312.06482] We study the possibility of measuring the optical depth at reionization without relying on large-scale Cosmic Microwave Background (CMB) polarization and obtain competitive measurements that can validate the state-of-the-art constraints on this parameter. Within the ΛCDM model, our most constraining result is τ=0.080±0.012, obtained by combining Planck temperature and polarization data at ℓ>30, the Atacama Cosmology Telescope (ACT) and Planck measurements of the lensing potential, Baryon Acoustic Oscillations (BAO), and Type-Ia supernova data from the Pantheon+ catalogue. Notably, using only ACT temperature, polarization, and lensing data in combination with BAO and supernovae, we obtain τ=0.076±0.015, which is entirely independent of Planck.

My Contribution: I performed the MCMC analysis for all the different combinations of datasets, realized all figures and tables and contributed to the paper writing.

### Hints of Neutrino Dark Matter scattering in the CMB? Constraints from the Marginalized and Profile Distributions

William Giarè, Adrià Gomez-Valent, Eleonora Di Valentino, Carsten van de Bruck[Accepted for publication in Phys. Rev. D][arXiv:2311.09116 ] We study scatter-like interactions between neutrinos and dark matter in light of different combinations of temperature, polarization and lensing data released by three independent CMB experiments: the Planck satellite, the Atacama Cosmology Telescope, and the South Pole Telescope. We apply two different statistical methodologies and, alongside the usual marginalization technique, we cross-check all the results through a Profile Likelihood analysis. Both methods confirm a mild preference for non-vanishing interactions from small-scale CMB data both when neutrinos are considered massless or massive particles. The Profile Likelihood analysis also confirms that interactions are not disfavoured by Planck.

My Contribution: I performed the MCMC analysis for all the different combinations of datasets and contributed to the paper writing.

### A Look Beyond ΛCDM: the quest for a more comprehensive model of cosmology

William Giarè[Conference proceeding, contribution to CORFU2022][ PoS CORFU2022 (2023) 25] This contribution aims to present a comprehensive and up-to-date overview of the situation emerging from the most recent analyses of the Cosmic Microwave Background temperature anisotropies and polarization angular power spectra examining the key elements underlying current discrepancies and the challenges that must be addressed to restore cosmic concordance.

### The state of the dark energy equation of state circa 2023

Luis A. Escamilla, William Giarè, Eleonora Di Valentino, Rafael C. Nunes, Sunny Vagnozzi[arXiv:2307.14802] This paper investigates the current limitations on the equation of state for dark energy. We specifically focus on the apparent inclination towards phantom dark energy observed in Planck Cosmic Microwave Background (CMB) data alone. We thoroughly examine the origins of this inclination and attribute it to various physical and geometrical factors. To establish a reliable conclusion, we combine data from Planck CMB, Baryon Acoustic Oscillations, Type Ia Supernovae, and Cosmic Chronometers, which yields a consensus dataset consistent with the cosmological constant value. In summary, although there are a few sporadic indications, we do not find any compelling evidence that steers us away from the cosmological constant.

My Contribution: I realized half of the MCMC analyses based on the CMB data in Table 2. I conducted the MCMC analyses for various combinations of CMB and local probes data as presented in Table 3. I produced all the plots from Fig. 1 to Fig. 7. I actively participated in the writing of the paper.

### On the lensing impact on cosmic relics & tensions

William Giarè, Olga Mena, Eleonora Di Valentino[Phys.Rev.D 108 (2023) 10, 103539 ][arXiv:2307.14204] This study explores late-time hot relic mass constraints using lensing data from the Atacama Cosmology Telescope, combined with data from the Planck Satellite and other local probes such as Baryon Acoustic Oscillations measurements, shear-shear, galaxy-galaxy, and galaxy-shear correlation functions from the Dark Energy Survey, as well as distance moduli measurements from Type Ia Supernovae. The tightest bounds obtained are stronger than laboratory neutrino mass searches, reaffirming the reliability of extracting thermal relic properties using cosmological observations. Finally, we present a discussion concerning the implications of the results on cosmic tensions.

My Contribution: I performed the MCMC analysis and realized all plots and tables. I contributed to the paper writing.

### Tracking the Multifield Dynamics with Cosmological Data: A Monte Carlo approach

William Giarè, Mariaveronica De Angelis, Carsten van de Bruck, Eleonora Di Valentino[JCAP 12 (2023) 014][arXiv:2306.12414] This paper introduces a numerical method for investigating multifield models of inflation. The algorithm solves the field equations throughout the entire inflationary period, predicting observable quantities such as scalar perturbations and gravitational waves. It incorporates the transfer matrix formalism to track the behaviour of modes on super-horizon scales and entropy transfer. The algorithm is integrated with Boltzmann codes to compute the full cosmology, including CMB anisotropies and polarization. A novel sampling algorithm efficiently explores the parameter space, enabling Monte Carlo analysis. The method is tested on a specific model, deriving constraints on its parameters.

My Contribution: I contributed to the theory code, interfaced it with Boltzmann integrator codes, and developed the sampler and the data analysis pipeline. I contributed to the paper writing.

### CMB Anomalies and the Hubble Tension

William Giarè [Invited chapter for the book "Hubble Constant Tension"] [arXiv:2305.16919] The standard model of cosmology is largely successful in describing many observations, including precise measurements of the Cosmic Microwave Background (CMB) radiation. However, some intriguing anomalies remain currently unexplained within this theoretical framework. Such discrepancies can be broadly categorized into two groups: those involving CMB-independent probes and those within different CMB experiments. Examples of the former category include the Hubble tension between the value of the present-day expansion rate of the Universe inferred by CMB observations and local distance ladder measurements. The latter category involves anomalies between the values of cosmological parameters obtained by different CMB experiments and their consistency with the predictions of ΛCDM. In this chapter, we primarily focus on this second category and study the agreement among the most recent CMB measurements to d the limitations and uncertainties underlying both the current data and the cosmological model. Finally, we discuss the implications for the Hubble tension and its proposed solutions.

Note: Invited chapter for the edited book "Hubble Constant Tension" (Eds. E. Di Valentino and D. Brout, Springer Singapore, expected in 2024)

### Inflationary Potential as seen from Different Angles: Model Compatibility from Multiple CMB Missions

William Giarè, Supriya Pan, Eleonora Di Valentino, Weiqiang Yang, Jaume de Haro, Alessandro Melchiorri[JCAP 09 (2023) 019] [arXiv:2305.15378] The absence of a definitive detection of B-mode polarization and the emerging discrepancies among different CMB experiments present a challenge in determining precise predictions for the inflationary models that best explain the observed data. In this work, we further explore this difficulty and conduct a case study by analyzing four well-known inflationary potentials in light of the most recent CMB observations released by Planck and ACT, along with B-modes polarization data from the BICEP Collaboration, and measurements of Baryon Acoustic Oscillations (BAO) and Redshift Space Distortions (RSD) from BOSS DR12 and eBOSS DR16. We show that the most typical models such as Starobisnky and α-attractors are in disagreement with the ACT small-scale CMB measurements, particularly when combined with B-modes polarization data. On the other hand, these potentials are in perfect agreement with the Planck measurements at larger angular scales. This dichotomy makes it challenging to identify a single model or a group of models that can be universally considered as the preferred choice based on all available CMB observations.

My contribution: I performed the data-analysis of the different potentials; I realized figure 1 and contributed to the paper writing.

### Impact of the damping tail on neutrino mass constraints

Eleonora Di Valentino, Stefano Gariazzo, William Giarè, Olga Mena,[Phys.Rev.D 108 (2023) 8, 083509][arXiv:2305.12989] We present up-to-date limits on neutrino masses and abundances exploiting either the Data Release 4 of the Atacama Cosmology Telescope (ACT) or the South Pole Telescope polarization measurements from SPT-3G, envisaging different non-minimal background cosmologies and marginalizing over them. Our model-independent mass limits assess the robustness of current cosmological measurements of the neutrino mass scale as well as the consistency between high-multipole and low-multiple Cosmic Microwave Background observations measuring such scale.

My contribution: I contributed to the data analysis for all the different cosmological models and to the bayesian model comparison; I contributed to the paper writing.

### Extended Analysis of Neutrino-Dark Matter Interactions with Small-Scale CMB Experiments

Philippe Brax, Carsten van de Bruck, Eleonora Di Valentino, William Giarè, Sebastian Trojanowski[Phys.Dark Univ. 42 (2023) 101321] [arXiv:2305.01383] We extend our analysis of neutrino Dark Matter interactions with small-scale CMB measurements [arXiv:2303.16895] by further proving the robustness of a preference (at 1σ level) for a non-zero coupling between the two species obtained by ACT as well as its combination with Planck and BAO. Our results are confirmed both by assuming a temperature-independent and T-squared-dependent cross-section as well as by fixing and relaxing the effective number of relativistic degrees of freedom in the early Universe. When performing a Bayesian model comparison, the interacting scenario is mostly preferred over a baseline ΛCDM cosmology. The preferred value of the interaction strength is used as a benchmark and the potential implications of dark matter's interaction with a sterile neutrino are discussed.

My contribution: I performed the cosmological data analyses for the νDM interactions, and realized figures 1-4 & 8-11. I contributed to the paper writing.

### New Insight on ν-DM Interactions

Philippe Brax, Carsten van de Bruck, Eleonora Di Valentino, William Giarè, Sebastian Trojanowski[MNRAS (letters) 527 (2023) 1, L122-L126][arXiv:2303.16895] We revisit the possibility of using cosmological observations to constrain models that involve interactions between neutrinos and dark matter. We show that small-scale measurements of the cosmic microwave background with a few per cent accuracy are critical for uncovering unique signatures from models with tiny couplings that would require a much higher sensitivity at lower multipoles, such as those probed by the Planck satellite. We analyze the high-multipole data released by the Atacama Cosmology Telescope, both independently and in combination with Planck and Baryon Acoustic Oscillation measurements, finding a compelling preference for a non-vanishing coupling which aligns with other CMB-independent probes. We illustrate how this coupling could be accounted for in the presence of dark matter interactions with a sterile neutrino.

My contribution: I performed the cosmological data-analyses for the νDM interactions, I realized figure 1 and figure 2, and I contributed to the paper writing.

### A Consistent View of Interacting Dark Energy from Multiple CMB Probes

Yuejia Zhai, William Giarè, Carsten van de Bruck, Eleonora Di Valentino,Olga Mena, Rafael C. Nunes[JCAP 07 (2023) 032] [arXiv:2303.08201] We analyze a cosmological model featuring an interaction between dark energy and dark matter in light of the measurements of the Cosmic Microwave Background released by three independent experiments: the Planck satellite, the Atacama Cosmology Telescope, and WMAP (9-year data). We show that different combinations of the datasets provide similar results, always favouring an interacting dark sector with a 95% CL significance in the majority of the cases. Remarkably, such a preference remains consistent when cross-checked through independent probes, while always yielding a value of the expansion rate consistent with the local distance ladder measurements.

My contribution: I contributed to the MCMC analyses for the different data-sets, I realized the bayesian model comparison, realized figure 1 and figure 2 and contributed to the paper writing.

### Exploring the H0 tension and the evidence for dark sector interactions from 2D BAO measurements

Armando Bernui, Eleonora Di Valentino, William Giarè, Suresh Kumar, Rafael C. Nunes[Phys.Rev.D 107 (2023) 10, 103531] [arXiv:2301.06097] We explore observational constraints on a cosmological model with an interaction between dark energy (DE) and dark matter (DM). By using a compilation of 15 measurements of the 2D BAO (i.e., transversal) scale in combination with Planck-CMB data, we explore the parametric space of a class of interacting DE models (IDE) showing that Planck-CMB + 2D BAO measurements provide a strong statistical evidence in favor of IDE cosmologies, offering a potential solution to the H0 tension.

My contribution: I contributed to the MCMC analyses for the different cosmological and astrophysical data-sets, I contributed to the bayesian model comparison, I realized figure 1 and contributed to the paper writing.

# 2022

### A novel model-marginalized cosmological bound on the QCD axion mass

Eleonora Di Valentino, Stefano Gariazzo, William Giarè, Alessandro Melchiorri, Olga Mena, Fabrizio RenziPhys.Rev.D 107 (2023) 10, 103528 [arXiv:2212.11926] We present strong model-marginalized limits on both thermal neutrinos and thermal QCD axions. Novel aspects of our analyses are the marginalization over several background cosmologies and the inclusion of small-scale Cosmic Microwave Background observations from the Atacama Cosmology Telescope and the South Pole Telescope, together with those from the Planck satellite and Baryon Acoustic Oscillation data.

My contribution: I contributed to a modified version of the code CAMB able to compute the thermal axion cosmology, I contributed to the data analysis for all the different cosmological models, I contributed to the bayesian model comparison, I realized figure 1 and figure 3; I contributed to the paper writing.

### Towards a reliable calculation of relic radiation from primordial gravitational waves

William Giarè, Matteo Forconi, Eleonora Di Valentino, Alessandro MelchiorriMNRAS 520 (2023) 2, 1757–1773 [arXiv:2210.14159]We revisit the calculation of relic radiation from primordial gravitational waves discussing some caveats of the state-of-the-art analyses. Through a parametric investigation, we demonstrate that the calculation is dominated by the behaviour of the tensor spectrum on scales where the slow-roll dynamics break down and the production of gravitational waves becomes model dependent. Motivated by these results, we realize a theoretical Monte Carlo and, working within the framework of the Effective Field Theory of inflation, we investigate the observable predictions of a very broad class of models proving the calculation to be remarkably model-dependent. We, therefore, conclude that accurate analyses are needed to infer reliable information on the inflationary Universe.

My Contribution: I performed the parametric analysis; developed the algorithm for integrating the Hubble Flow Equations; contributed to derive the results from the theoretical Monte Carlo, derived the updated bounds on inflation from the BBN; realised all the plots in the paper; and contributed to the paper writing.

### Revealing the effects of curvature on the cosmological models

Weiqiang Yang, William Giarè, Supriya Pan, Eleonora Di Valentino, Alessandro Melchiorri, Joseph SilkPhys.Rev.D 107 (2023) 6, 063509 [arXiv:2210.09865] We systematically explore the effects of adding curvature in extended cosmologies involving a free-to-vary neutrino sector and different parametrizations of Dark Energy showing that forcing the Universe to be flat can significantly bias the constraints on the equation of state of the DE component and its dynamical nature.

My contribution: I contributed to the analyses and to the result's discussion; I realized figures 17-22 and contributed to the paper writing.

### Is the Harrison Zel'dovich spectrum coming back? ACT preference for ns~1 and its discordance with Planck

William Giarè, Fabrizio Renzi, Olga Mena, Eleonora Di Valentino, Alessandro MelchiorriMNRAS 521 (2023) 2, 2911–2918 [arXiv:2210.09018] We explore yet a new potential challenge for inflationary cosmology arising from Planck-independent observations of the cosmic microwave background. Namely the ∼ 2.7σ discrepancy in the value of the scalar spectral index measured by Planck (ns = 0.9649 ± 0.0044) and by the Atacama Cosmology Telescope (ACT) (ns = 1.008 ± 0.015). We show that this discrepancy is neither alleviated with the addition of large-scale structure information nor with the low multipole polarization data. We discuss possible avenues to alleviate the tension relying on either neglecting polarization measurements from ACT or in extending different sectors of the theory

My contribution: I performed the MCMC analyses, realized all the figures and contributed to the paper writing.

### Quantifying the global ‘CMB tension’ between the Atacama Cosmology Telescope and the Planck satellite in extended models of cosmology

Eleonora Di Valentino, William Giarè, Alessandro Melchiorri, Joseph SilkMNRAS 520 (2023) 1, 210–215 [arXiv:2209.14054] We study the global agreement between the most recent observations of the Cosmic Microwave Background temperature and polarization anisotropies angular power spectra released by the Atacama Cosmology Telescope and the Planck satellite in various extended cosmological models. By using the Suspiciousness statistic, we show that the global "CMB tension" between the two experiments, quantified at the Gaussian equivalent level of ∼2.5σ within the baseline ΛCDM, is reduced at the level of 1.8σ when the effective number of relativistic particles is significantly less than the standard value, while it ranges between 2.3σ and 3.5σ in all the other extended models.

My contribution: I wrote the pipeline for the suspiciousness , contributed to the data analysis , I realized figure 1; I contributed to the paper writing.

### Health checkup test of the standard cosmological model in view of recent Cosmic Microwave Background Anisotropies experiments

Eleonora Di Valentino, William Giarè, Alessandro Melchiorri, Joseph SilkPhys. Rev. D 106, 103506 [arXiv:2209.12872] We present an updated data-analysis comparison of the most recent observations of the Cosmic Microwave Background temperature anisotropies and polarization angular power spectra released by four different experiments: the Planck satellite on one side, and the Atacama Cosmology Telescope (ACTPol) and the South Pole Telescope (SPT-3G), combined with the WMAP satellite 9-years observation data on the other side. We investigate in a systematic way many extended cosmological models providing several hints for anomalies in the CMB angular power spectra in tension with the standard cosmological model. This indicates that either significant unaccounted-for systematics in the data are producing biased results or that ΛCDM is an incorrect/incomplete description of Nature.

My contribution: I contributed to the data analysis , I realized figures 13-18; I contributed to the paper writing.

### Cosmological Bound on the QCD Axion Mass, Redux

Francesco D'Eramo, Eleonora Di Valentino, William Giarè, Fazlollah Hajkarim, Alessandro Melchiorri, Olga Mena, Fabrizio Renzi, Seokhoon YunJCAP 09 (2022) 022 [arXiv:2205.07849] We revisit the joint constraints in the mixed hot dark matter scenario in which both thermally produced QCD axions and relic neutrinos are present. In light of recent advances in literature, we recompute the cosmological axion abundance and improve the state-of-the-art analyses by avoiding approximate methods, such as the instantaneous decoupling approximation, and limitations due to the limited validity of the perturbative approach in QCD that forced to artificially divide the constraints from the axion-pion and the axion-gluon production channels. Investigating the two most popular axion frameworks ( the KSVZ and DFSZ axion) we find robust and self-consistent limits on the QCD axion mass that are approximately a factor of 5 more constraining with respect to the existing limits.

My contribution: I contributed to a modified version of the code CAMB able to compute the thermal axion cosmology and address the new advances in literature; I contributed to compute the BBN predictions and to include them in CAMB; I contributed to the realization of the likelihoods for future CMB-S4-like and BAO DESI-like experiments; I contributed to the algorithms and the methodology used for the data analysis; I carried out the analysis of the BBN data; I contributed to the analysis of the CMB and BAO data (and the CMB-S4 and DESI forcasted data); I realized all the tables and figures; I contributed to the paper writing.

### Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies

Snowmass CollaborationJ. High En. Astrophys. 2204, 002 (2022) [arXiv:2203.06142] Snowmass Collaboration paper on cosmological tensions and anomalies.

# 2021

### Relics from the Early Universe: Primordial Gravitational Waves, Axions and Neutrinos

William Giarè,My PhD ThesisMy PhD Thesis

### The resilience of the Etherington-Hubble relation

Fabrizio Renzi, Natalie B. Hogg , William Giarè,MNRAS 513 (2022) 3, 4004–4014 [arXiv:2112.05701] We make use of the Etherington reciprocity theorem, or distance duality relation (DDR), to build a consistency check for extended cosmological models. We provide the first joint measurement of the Hubble constant (H0) and DDR to percentage accuracy and find a mild 2 sigma discrepancy between the latest SH0ES measurement of H0 and the validity of the DDR. Then, we outline our consistency check methodology for extended cosmological models, finding that models with non-zero spatial curvature show a preference for DDR violation at the level of 1.5 sigma.

My contribution: I contributed to the codes used for constraining H0 and DDR, I contributed to outline the consistency check methodology and I analyzed the different models discussed in Sec. IV.2. I realized Fig3. I contributed to the paper writing.

### Cosmological forecasts on thermal axions, relic neutrinos and light elements

William Giarè, Fabrizio Renzi, Alessandro Melchiorri, Olga Mena and Eleonora Di Valentino,MNRAS 511 (2022) 1, 1373-1382 [arXiv:2110.00340] We study how the improvements expected by future Cosmic Microwave Background and Baryon Acoustic Oscillation measurements can be translated into constraining power for well motivated extensions of the Standard Model of elementary particles that involve axions thermalized before the QCD phase transition by scatterings with gluons in combination with neutrinos and primordial BBN elements.

My contribution: I implemented the code for axion-gluon interactions inside CAMB, I contributed to the realization of the likelihoods for future CMB-S4-like and BAO DESI-like experiments; I contributed to the modification of CAMB to include all the BBN primordial elements. I analyzed the simulated data and realized Figs. 2 and 3. I contributed to the paper writing.

### Cosmological constraints on slow-roll inflation: an update

Matteo Forconi, William Giarè, Eleonora Di Valentino, Alessandro Melchiorri Phys.Rev D 104, 103528 [arXiv:2110.01695]In light of the most recent cosmological observations, we provide new updated constraints on the slow-roll inflation in different extended scenarios beyond the ΛCDM cosmological model. We interpret the results under the framework of the different inflationary models proposed in literature, showing how the differences in the datasets can change the compatibility among the different models, sometimes leading to discordant conclusions.

My Contribution: I analyzed the different datasets, realized the triangular plots and contributed to the paper writing.

# 2020

### New cosmological bounds on hot relics: axions & neutrinos

William Giarè, Eleonora Di Valentino, Alessandro Melchiorri, Olga MenaMNRAS 505 (2021) 2, 2703–2711 [arXiv:2011.14704] In light of the most recent cosmological observations we analyze a realistic mixed hot-dark-matter scenario which includes axions and massive neutrinos as additional thermal species. For the axion thermalization in the early Universe, we consider both the axion-gluon scattering and the axion-pion scattering. For the latter process we remain in the range of validity of chiral perturbation theory and we don't assume any specific model for axion interactions.

My contribution: I implemented the code for axion-pion and axion-gluon interactions inside CAMB, l realized Figs. 1 and 3 and contributed to the data analysis and to the paper writing.

### Higher-curvature corrections and tensor modes

William Giarè, Fabrizio Renzi, Alessandro Melchiorri Phys.Rev D 103, 043515 [arXiv:2012.00527]We study the effects of a coupling of the inflaton field to higher-curvature tensors in models of inflation with a minimal breaking of conformal symmetry. We show that an observable violation of the inflationary consistency relation(s) from higher-curvature tensors implies also a relatively large scale dependence of the tensor tilt. We discuss the implications for the observational constraints.

My contribution: I developed the theoretical model and performed the theoretical calculations. I contributed to the data analysis and I realized Figs. 1 and 3. I contributed to the paper writing.

### Propagating speed of primordial gravitational waves

William Giarè, Fabrizio Renzi Phys. Rev. D 102, 083530 [arXiv:2007.04256] We study the effects of a non-trivial gravity propagation during inflation. We discuss the implications for the stochastic background of inflationary gravitational waves both from the theoretical side and on the data analysis perspective.

My Contribution: I developed the theoretical model and performed the theoretical calculations. I contributed to the data analysis and to the paper writing.

### Probing the inflationary background of gravitational waves from large to small scales

William Giarè, Alessandro MelchiorriPhys. Lett. B 815 (2021) 136137 [arXiv:2003.04783]We show that due to the huge difference in the scales probed by CMB and GW experiments, higher-order terms in the primordial tensor spectrum, albeit negligibly small on the CMB scales, may give non-negligible contributions on the scale probed by direct gravitational observations. We discuss the implications for the constraints on the tensor tilt.

My Contribution: I derived the results, realized the figures and contributed to the paper writing.

# 2019

### Testing the inflationary slow-roll condition with tensor modes

William Giarè, Eleonora Di Valentino, Alessandro MelchiorriPhys. Rev. D 99, 123522We investigate the higher-order slow-roll consistency relations among scalar and tensor parameters. We show that a set of slow roll consistency relations can be derived at any order in the power-law expansion, discussing the implications both from a theoretical point of view and on a data analysis perspective.

My contribution: I derived the results, analyzed the data, realized the figures and contributed to the paper writing.