Acoustic Oscillations Research Articles

Evolution of the Universe with quintessence model in Rastall gravity

Abstract We investigate the Universe’s evolution within the framework of Rastall gravity, which is an extension of the standard ΛCDM model. Utilizing a linear parametrization of the Equation of State (EoS) in a Friedmann-Lemaître-Robertson-Walker (FLRW) background, we constrain the model parameters through analysis of cosmic chronometers (CC), Pantheon, Gold, Gamma Ray Burst (GRB), and Baryon Acoustic Oscillations (BAO) datasets, as well as their joint analysis, under 1σ and 2σ confidence levels, considering the Rastall parameter λ. The constrained parameters are then used to compare our model with the standard ΛCDM model. Our findings include a detailed examination of the model’s physical interpretations and demonstrate the potential for an accelerating universe expansion in later times, aligning with the observed behavior of dark energy.

Cascading Dark Energy

The standard cosmological model is in the midst of a stress test, thanks to the tension between supernova-based measurements of the Hubble constant H 0 and inferences of its values from cosmic microwave background (CMB) anisotropies. Numerous explanations for the present-day cosmic acceleration require the presence of a new fundamental scalar field, as do early dark energy solutions to the Hubble tension. This raises the possibility that multiple fields cooperatively contribute to the dark energy component in bursts throughout cosmic time due to distinct initial conditions and couplings. Here, this cascading dark energy scenario is illustrated through a realization that effectively reduces to a two-field model, with two epochs in which dark energy is cosmologically significant. The model is compared to measurements of the CMB and baryon acoustic oscillations, as well as both PANTHEON and SH0ES observations of Type Ia supernovae. Neglecting the linear perturbations, it is found that this scenario ameliorates the Hubble tension, improving over purely late-time models of dark energy and the agreement between the galaxy survey measurements of baryon acoustic oscillations.

2D BAO vs. 3D BAO: Solving the Hubble Tension with Bimetric Cosmology

Ordinary 3D Baryon Acoustic Oscillations (BAO) data are model-dependent, requiring the assumption of a cosmological model to calculate comoving distances during data reduction. Throughout the present-day literature, the assumed model is ΛCDM. However, it has been pointed out in several recent works that this assumption can be inadequate when analyzing alternative cosmologies, potentially biasing the Hubble constant (H0) low, thus contributing to the Hubble tension. To address this issue, 3D BAO data can be replaced with 2D BAO data, which are only weakly model-dependent. The impact of using 2D BAO data, in combination with alternative cosmological models beyond ΛCDM, has been explored for several phenomenological models, showing a promising reduction in the Hubble tension. In this work, we accommodate these models in the theoretically robust framework of bimetric gravity. This is a modified theory of gravity that exhibits a transition from a (possibly) negative cosmological constant in the early universe to a positive one in the late universe. By combining 2D BAO data with cosmic microwave background and type Ia supernovae data, we find that the inverse distance ladder in this theory yields a Hubble constant of H0=(71.0±0.9)km/s/Mpc, consistent with the SH0ES local distance ladder measurement of H0=(73.0±1.0)km/s/Mpc. Replacing 2D BAO with 3D BAO results in H0=(68.6±0.5)km/s/Mpc from the inverse distance ladder. We conclude that the choice of BAO data significantly impacts the Hubble tension, with ordinary 3D BAO data exacerbating the tension, while 2D BAO data provide results consistent with the local distance ladder.

Quadratic Frequency Dispersion in the Oscillations of Intermediate-mass Stars

Asteroseismology, the study of stellar vibration, has met with great success, shedding light on stellar interior structure, rotation, and magnetism. Prominently known as δ Scutis, the intermediate-mass main-sequence oscillators that often exhibit rapid rotation and possess complex internal stratification are important targets of asteroseismic study. δ Scuti pulsations are driven by the κ (opacity) mechanism, resulting in a set of acoustic modes that can be challenging to interpret. Here, we apply machine learning to identify new patterns in the pulsation frequencies of δ Scuti stars, discovering resonances spaced according to quadratic functions of integer mode indices. This unusual connection between mode frequencies and indices suggests that rotational influence may play an important role in determining the frequencies of these acoustic oscillations.

Phantom Matter: A Challenging Solution to the Cosmological Tensions

The idea of composite dark energy (DE) is quite natural since on general grounds we expect that the vacuum energy density (associated with the cosmological term Λ) may appear in combination with other effective forms of DE, denoted X. Here we deal with model wXCDM, a simplified version of the old ΛXCDM model, and exploit the possibility that X behaves as “phantom matter” (PM), which appears in stringy versions of the running vacuum model (RVM). Unlike phantom DE, the PM fluid satisfies the strong energy condition like usual matter, hence bringing to bear positive pressure at the expense of negative energy. Bubbles of PM may appear in the manner of a transitory “phantom vacuum” tunneled into the late Universe before it heads toward a new de Sitter era, thereby offering a crop field for the growing of structures earlier than expected. Using Type Ia supernovae, cosmic chronometers, transversal baryon acoustic oscillations (BAO 2D), large-scale structure data, and the full cosmic microwave background likelihood from Planck 2018, we find that the H 0 and growth tensions virtually disappear, provided that BAO 2D are the only source of BAO data used in the fit. In contrast, our preliminary analysis using exclusively anisotropic BAO (BAO 3D) indicates that the ability to ease the H 0 tension is significantly reduced as compared to the scenario with BAO 2D, despite the fact that the overall fit to the cosmological data is still better than in the ΛCDM. Finally, our approach with BAO 2D favors quintessence-like behavior of the DE below z ≃ 1.5 at ≳3σ confidence level, which is compatible with the recent DESI measurements.

Response of n-Heptane and Dodecane Swirl-Stabilized Spray Flames to Transverse Forcing Characterized By Flame Describing Functions Based on Downstream Acoustic Pressure or Velocity Signals

Abstract Predicting thermoacoustic instabilities in annular combustors requires knowledge of the impact of acoustic oscillations on heat release rate oscillations. Flame Describing Functions (FDF) measured at the burner exit using acoustic forcing are key elements of thermoacoustic instability analyses. FDFs based on acoustic pressure measurements, FP' or on axial velocity measurements FU', are compared here. This study is done on the TACC-Spray bench, an original linear array of spray flames stabilized by a strong swirling flow, representing an unfolded sector of a self-unstable annular combustor. Acoustic forcing of a standing transverse chamber mode is applied downstream of the injectors. Experiments are conducted with liquid n-heptane or dodecane, with the flames placed at a pressure or an intensity antinode of the transverse mode. FP' does not depend on the measurement location for acoustically-compact flames provided that this location remains in the flame vicinity. FU' can lead to significant discrepancies, as swirling flows present strong velocity gradients, which can be minimized by carefully choosing the measurement location. The injector admittance linking the two FDFs is shown to be quasi-independent of the forcing amplitude here. Consequently, both FDFs show a similar dependence on the forcing amplitude. FP' indicates constructive combustion-acoustics interference whatever the flame location in the acoustic field and the fuel, consistent with self-sustained instabilities observed in the annular combustor. An analysis using the Rayleigh criterion corroborates the results derived from the FDFs. So, FP' appears as a powerful and practical tool for characterizing combustion dynamics.

The role of LRG1 and LRG2’s monopole in inferring the DESI 2024 BAO cosmology

ABSTRACT The Dark Energy Spectroscopic Instrument (DESI) collaboration recently released its first year of data (DR1) on baryon acoustic oscillations (BAO) in galaxy, quasar, and Lyman-$\alpha$ forest tracers. When combined with cosmic microwave background (CMB) and Type Ia supernovae (SNIa) data, DESI BAO results suggest potential thawing behaviour in dark energy. Cosmological analyses utilize comoving distances along ($D_\mathrm{ H}$) and perpendicular to ($D_\mathrm{ M}$) the line of sight. Notably, there are $1\sim 2\sigma$ deviations in $D_\mathrm{ M}$ and $D_\mathrm{ H}$ from Planck cosmology values in the luminous red galaxies (LRG) bins LRG1 and LRG2.This study examines the role of LRG1 and LRG2 in diverging DESI 2024 BAO cosmology from Planck cosmology. We use angle-averaged distance $D_\mathrm{ V}$ and the ratio $F_{\rm AP}=D_\mathrm{ M}/D_\mathrm{ H}$, which are more directly related to the measured monopole and quadrupole components of the galaxy power spectrum or correlation function, instead of the officially adopted $D_\mathrm{ M}$ and $D_\mathrm{ H}$. This transformation aims to isolate the influence of monopoles in LRG1 and LRG2 on deviations from $w=-1$. Our findings indicate that removing the $D_\mathrm{ V}$ data point in LRG2 aligns DESI + CMB + SNIa data compilation with $w=-1$ within a $2\sigma$ contour and reduces the $H_0$ discrepancy from the Planck 2018 results from $0.63\sigma$ to $0.31\sigma$. Similarly, excluding the $D_\mathrm{ V}$ data point from LRG1 shifts the $w_0/w_a$ contour toward $w=-1$, although no intersection occurs. This highlights the preference of both LRG1 and LRG2 BAO monopole components for the thawing dark energy model, with LRG2 showing a stronger preference. We provide the $D_\mathrm{ V}$ and $F_{\rm AP}$ data and their covariance alongside this paper.

Geophysical effects caused by the bolide fall on September 02, 2023 (Turkey)

We present the results of instrumental observations of acoustic oscillations, geomagnetic variations and variations of the atmospheric electric field during the fall and explosive destruction of the bolide in the southeast of Turkey on September 02, 2023. It is shown that the destruction of the bolide under the action of aerodynamic forces, which occurred in three stages, was accompanied by an acoustic signal of a characteristic shape and manifested in variations of the magnetic and electric fields in the near-surface layer atmosphere. The total energy of the event, estimated by the acoustic effect, was ~ 9×1012 J, which corresponds to about 2.15 kt in TNT equivalent. The maximum amplitude of geomagnetic variations caused by the explosion of the bolide ranged from 0.2 to 2.1 nT depending on the distance. At the same time, the amplitude of variations of the vertical component of the atmospheric electric field at the Mikhnevo observatory (distance ~1900 km) was ~70 V/m. The ionospheric effect of the event under consideration is demonstrated in the form of variations of the critical frequency f0F2 obtained as a result of processing ionograms of height-frequency sounding of the ionosphere at the Rome station.

Forecasting Constraint on the f(R) Theory with the CSST SN Ia and BAO Surveys

Abstract The $f(R)$ modified gravity theory can explain the accelerating expansion of the late Universe without introducing dark energy. In this study, we predict the constraint strength on the $f(R)$ theory using the mock data generated from the China Space Station Telescope (CSST) Ultra-Deep Field (UDF) Type Ia supernova (SN Ia) survey and wide-field slitless spectroscopic baryon acoustic oscillation (BAO) survey. We explore three popular $f(R)$ models, and introduce a parameter $b$ to characterize the deviation of the f(R) theory from the $\Lambda$CDM theory. The Markov Chain Monte Carlo (MCMC) method is employed to constrain the parameters in the $f(R)$ models, and the nuisance parameters and systematical uncertainties are also considered in the model fitting process. Besides, we also perform model comparisons between the $f(R)$ models and the $\Lambda$CDM model. We find that the constraint accuracy using the CSST SN Ia+BAO dataset alone is comparable to or even better than the result given by the combination of the current relevant observations, and the CSST SN Ia+BAO survey can distinguish the $f(R)$ models from the $\Lambda$CDM model. This indicates that the CSST SN Ia and BAO surveys can effectively constrain and test the $f(R)$ theory.

Energy conversion performance in looped and stirling traveling-wave and standing-wave thermoacoustic engines

This present study conducts a comprehensive comparison of looped traveling-wave thermoacoustic engines (TWTAEs) and Stirling TWTAEs using two- and three-dimensional (2D and 3D) time-domain models. These models, validated through comparisons with existing experimental results, confirm the accuracy of our developed full-scale numerical TWTAE models. By evaluating the acoustic characteristics and comparing them with conventional standing-wave thermoacoustic engines, this work highlights the superior performance of the Stirling TWTAE. It achieves the highest heat-driven acoustic power and thermoacoustic energy conversion efficiency. This superior performance is attributed to its operation at a lower oscillation frequency (115 Hz) and an optimized phase between acoustic velocity and pressure oscillations (40 degrees). Additionally, our study explores rich nonlinear phenomena within the flow fields of the Stirling TWTAE. Notably, varying the temperature gradients between 410 K and 485 K introduces a bistable zone with distinct pressure amplitudes. Moreover, mass streaming under varying temperature gradients, and mode transitions due to external flow perturbations are observed inside the engine. These findings not only quantitatively confirm the high efficiency potential of the Stirling TWTAE but also demonstrate the effectiveness of CFD in the development of full-scale numerical models for predicting and optimizing the heat-driven acoustic characteristics and nonlinear phenomena of traveling-wave thermoacoustic systems.

Acoustically Induced Transparancy for Gamma-Ray Photons and Some of Its' Applications

In this paper, we consider the effect of the emergence of transparency of a resonantly absorbing medium for electromagnetic radiation due to the excitation of piston-like acoustic oscillations of the medium along the direction of radiation propagation – acoustically induced transparency. The physical mechanism and basic conditions for the implementation of the effect are discussed, as well as its application to reduce the propagation velocity of gamma-ray photons and on-demand recovery of an arbitrary part of a single-photon wave packet resonantly absorbed in the medium.

Alleviating the Hubble tension using the Barrow holographic dark energy cosmology with Granda–Oliveros IR cut-off

ABSTRACT In this study, we investigate the Barrow holographic dark energy (BHDE) model with the Granda–Oliveros(G–O) infrared (IR) cut-off in the presence of neutrino masses, utilizing the latest observational data to address the Hubble tension. The GO cut-off is defined as $L_{\mathrm{ IR}}=(\alpha H^2 + \beta \dot{H})^{-1/2}$. We place constraints on the total neutrino mass $\sum m_{\nu }$ using data from Type Ia supernovae (SN) Pantheon, cosmic chronometers (CC), cosmic microwave background (CMB), Baryon Acoustic Oscillation (BAO) data sets, and Planck Lensing. Specifically, the comprehensive CMB + BAO + CC + Pantheon data set provides a total neutrino mass of $0.118\, \text{eV}$. The parameters for the Barrow-GO model are determined to be $\Delta = 0.0055^{+0.0086}_{-0.0086}$, $\alpha = 0.997^{+0.060}_{-0.060}$, and $\beta = 0.598^{+0.080}_{-0.080}$, showing good agreement with previous studies. One of the key findings of this study is the model’s ability to alleviate the Hubble tension, as evidenced by the comparison of $H_0$ measurements. Specifically, the tension value for the combination of data set (CMB + BAO + CC + Pantheon + Lensing) is $1.5\sigma$ with the Planck 2018 and $1.4\sigma$ with R22. These results underscore the importance of multi-data set integration in refining constraints on neutrino properties and highlight the model’s efficacy in probing fundamental aspects of neutrino physics. Our results demonstrate that the BHDE model with the GO cut-off can effectively address the Hubble tension, offering a coherent framework that reconciles local and cosmological measurements of the Hubble constant.

Evaluating extensions to LCDM: an application of Bayesian model averaging and selection

We present a powerful and innovative statistical framework to address key cosmological questions about the universe's fundamental properties, performing Bayesian model averaging (BMA) and model selection. Utilizing this framework, we systematically explore extensions beyond the standard ΛCDM model, considering a varying curvature density parameter ΩK, a spectral index ns = 1 and a varying n run, a constant dark energy equation of state (EOS) w 0CDM and a time-dependent one w 0 w aCDM. We also assess cosmological data against a varying effective number of neutrino species N eff. Our analysis incorporates data from various combinations of cosmic microwave background (CMB) data from the latest Planck PR4 analysis, CMB lensing from Planck 2018, baryonic acoustic oscillations (BAO), and the Bicep-KECK 2018 results.We reinforce the standard ΛCDM model statistical preference when combining CMB data withCMB lensing, BAO, and Bicep-KECK 2018 data against the K-ΛCDM model anddns /d ln k-ΛCDM with a probability > 80%. Whenevaluating the dark energy EOS, we find that this dataset does not exhibit a strong preferencebetween the standard ΛCDM model and the constant dark energy EOS model w 0CDM,with a model posterior probability distribution of approximately ≈ 40%:60% in favour of w 0CDM, while the time-varying dark energy EOS model only holds below 1%probability. We find a similar result also when considering the N eff-ΛCDM model, with asplit probability almost 50%-50% from both our datasets.Overall, our application of BMA reveals that including model uncertainty in these cases does notsignificantly impact the Hubble tension, showcasing BMA's robustness and utility in cosmologicalmodel evaluation.

Investigating the Hubble tension and σ 8 discrepancy in f(Q) cosmology

In this study, we incorporated a three-parameter family, of the metric incompatible modification of standard general relativity ω models into the Boltzmann code MGCLASS at both the background and perturbation levels, in order to conduct a Bayesian study employing probes that include the cosmic microwave background (CMB), baryon acoustic oscillations (BAO), weak lensing (WL), alone or its correlation with galaxy clustering (3×2pt) and growth measurements f σ 8, for each submodel. Our analysis focused on the impact of the Hubble tension in H 0 and the discrepancy in σ 8 resulting from the inclusion of our model's parameters, namely M, α and β. We find that none of the sub models, considered alone or combined, were able of alleviating the Hubble tension with only reducing it to 3 σ in the least constraining, highest degree of freedom case while we found that the σ 8 discrepancy, already strongly mitigated on WL linear scales, especially when we let all our model's parameters as free, appears again when considering the more constraining 3×2pt probe. Among the parameters considered, we found that β, acting in scaling both the gravitational and the Hubble parameter, had the most impact in reducing the discrepancy, with data preferring far from ΛCDM alike values, before the combination with fσ 8 constrain it back to its general relativity values.

Towards a new model-independent calibration of Gamma-Ray Bursts

Current data on baryon acoustic oscillations and Supernovae of Type Ia (SNIa) cover up to z∼2.5. These low-redshift observations play a very important role in the determination of cosmological parameters and have been widely used to constrain the ΛCDM and models beyond the standard, such as the ones with open curvature. To extend this investigation to higher redshifts, Gamma-Ray Bursts (GRBs) stand out as one of the most promising observables. In spite of being transient, they are extremely energetic and can be used to probe the universe up to z∼9.4. They exhibit characteristics that suggest they are potentially standardizable candles and this allows their use to extend the distance ladder beyond SNIa. The use of GRB correlations is still a challenge due to the spread in their intrinsic properties. One of the correlations that can be employed for the standardization is the fundamental plane relation between the peak prompt luminosity, the rest-frame end time of the plateau phase, and its corresponding luminosity, also known as the three-dimensional Dainotti correlation. In this work, we propose an innovative method of calibration of the Dainotti relation which is independent of cosmology. We employ state-of-the-art data on Cosmic Chronometers (CCH) at z≲2 and use the Gaussian Processes Bayesian reconstruction tool. To match the CCH redshift range, we select 20 long GRBs in the range 0.553≤z≤1.96 from the Platinum sample, which consists of well-defined GRB plateau properties that obey the fundamental plane relation. To ensure the generality of our method, we verify that the choice of priors on the parameters of the Dainotti relation and the modelling of CCH uncertainties and covariance have negligible impact on our results. Moreover, we consider the case in which the redshift evolution of the physical features of the plane is accounted for. We find that the use of CCH allows us to identify a sub-sample of GRBs that adhere even more closely to the fundamental plane relation, with an intrinsic scatter of σint=0.20−0.05+0.03 obtained in this analysis when evolutionary effects are considered. In an epoch in which we strive to reduce uncertainties on the variables of the GRB correlations in order to tighten constraints on cosmological parameters, we have found a novel model-independent approach to pinpoint a sub-sample that can thus represent a valuable set of standardizable candles. This allows us to extend the cosmic distance ladder presenting a new catalogue of calibrated luminosity distances up to z=5.

Growth of cosmic perturbations in the modified [formula omitted] gravity

We explore the generalized f(R,T) modified theory of gravity, where the gravitational Lagrangian is a function of Ricci scalar R and the trace of the energy–momentum tensor T. We derive modified field equations to the linear order of perturbations in the context of f(R,T) model. We then investigate the growth of perturbations in the context of f(R,T) modified gravity. Primary numerical investigations based on matter power spectra diagrams indicate a structure growth suppression in f(R,T) gravity, which exhibits consistency with local measurements. Also, we notice that matter-geometry interaction in f(R,T) model would results in the specific feature named as ”matter acoustic oscillations” appeared in matter power spectra diagrams. Moreover, we put constraints on the cosmological parameters of f(R,T) model, utilizing current observations, chiefly cosmic microwave background (CMB), weak lensing, supernovae, baryon acoustic oscillations, and redshift-space distortions data. Numerical results based on MCMC calculations imply that f(R,T) is a qualified theory of modified gravity in reconciling Planck CMB data with local probes of large scale structures, by reporting lower values for the structure growth parameter σ8 compared to the standard model of cosmology.

Testing the standardizability of, and deriving cosmological constraints from, a new Amati-correlated gamma-ray burst data compilation

By using gamma-ray burst (GRB) data to simultaneously constrain Amati correlation parameters and cosmological parameters in six spatially flat and nonflat dark energy cosmological models, we show that an updated 220 GRB version of the Jia et al. [1] GRB data compilation are standardizable through the Amati correlation and so can be used for cosmological analyses. However, the resulting GRB data constraints on the current value of the nonrelativistic matter density parameter, Ω m 0, are in > 2σ tension with those from a joint analysis of better-established Hubble parameter [H(z)] and baryon acoustic oscillation (BAO) data for most of the cosmological models we consider, indicating that these GRB data cannot be jointly used with better-established H(z) + BAO data to constrain cosmological parameters.

Robust preference for Dynamical Dark Energy in DESI BAO and SN measurements

Recent Baryon Acoustic Oscillation (BAO) measurements released by DESI, when combined with Cosmic Microwave Background (CMB) data from Planck and two different samples of Type Ia supernovae (Pantheon-Plus and DESY5) reveal a preference for Dynamical Dark Energy (DDE) characterized by a present-day quintessence-like equation of state that crossed into the phantom regime in the past. A core ansatz for this result is assuming a linear Chevallier-Polarski-Linder (CPL) parameterization w(a) = w 0 + wa (1-a) to describe the evolution of the DE equation of state (EoS). In this paper, we test if and to what extent this assumption impacts the results. To prevent broadening uncertainties in cosmological parameter inference and facilitate direct comparison with the baseline CPL case, we focus on 4 alternative well-known models that, just like CPL, consist of only two free parameters: the present-day DE EoS (w0 ) and a parameter quantifying its dynamical evolution (wa ). We demonstrate that the preference for DDE remains robust regardless of the parameterization: w0 consistently remains in the quintessence regime, while wa consistently indicates a preference for a dynamical evolution towards the phantom regime. This tendency is significantly strengthened by DESY5 SN measurements. By comparing the best-fit χ2 obtained within each DDE model, we notice that the linear CPL parameterization is not the best-fitting case. Among the models considered, the EoS proposed by Barboza and Alcaniz consistently leads to the most significant improvement.

DESI dark energy time evolution is recovered by cosmologically coupled black holes

Recent baryon acoustic oscillation (BAO) measurements by the Dark Energy Spectroscopic Instrument (DESI) provide evidence that dark energy (DE) evolves with time, as parameterized by a w 0 w a equation of state. Cosmologically coupled black holes (BHs) provide a DE source that naturally evolves with time, because BH production tracks cosmic star-formation. Using DESI BAO measurements and priors informed by Big Bang Nucleosynthesis, we measure the fraction of baryonic density converted into BHs, assuming that all DE is sourced by BH production. We find that the best-fit DE density tracks each DESI best-fit w 0 w a model within 1σ, except at redshifts z ≲ 0.2, highlighting limitations of the w 0 w a parameterization. Cosmologically coupled BHs produce H 0 = (69.94 ± 0.81) km s-1 Mpc-1, with the same χ 2 as ΛCDM, and with two fewer parameters than w 0 w a . This value reduces tension with SH0ES to 2.7σ and is in excellent agreement with recent measurements from the Chicago-Carnegie Hubble Program. Because cosmologically coupled BH production depletes the baryon density established by primordial nucleosynthesis, these BHs provide a physical explanation for the “missing baryon problem” and the anomalously low sum of neutrino masses preferred by DESI.The global evolution of DE is an orthogonal probe of cosmological coupling, complementing constraints on BH mass-growth from elliptical galaxies, stellar binaries, globular clusters, the LIGO-Virgo-KAGRA merging population, and X-ray binaries.A DE density that correlates with cosmic star-formation: 1) is a natural outcome of cosmological coupling in BH populations; 2) eases tension between early and late-time cosmological probes; and 3) produces time-evolution toward a late-time ΛCDM cosmology different from Cosmic Microwave Background projections.

Evolution of coupled scalar perturbations through smooth reheating. Part I. Dissipative regime

If the inflaton is a heavy scalar field, it may equilibrate slower thansome other degrees of freedom, e.g. non-Abelian gauge bosons. In this case,perturbations in the inflaton field and in a thermalplasma coexist from a given moment onwards. We derive a gauge-invariant setof three coupled equations governing the time evolution of such a system.Despite singular coefficients,a reliable numerical solution can be obtained for a longtime period, starting from phase oscillations inside the Hubble horizon,and extending until acoustic oscillations in a radiation-dominated universe.Benchmarks are illustrated from a “weak regime”,where perturbations have a quantum-mechanical origin but get dissipatedby interactions with the plasma. Among applications of our formalismcould be inhomogeneity-induced nucleations inpost-inflationary phase transitions, andthe production of scalar-induced gravitational waves.