Thermal inflation, a brief low energy inflation after the primordial inflation, resolves the moduli problem in the context of supersymmetric cosmology. In the thermal inflation scenario, the primordial power spectrum is modestly redshifted on large scales, but suppressed by a factor of 1/50 on scales smaller than the horizon size at the beginning of thermal inflation. We compare the thermal inflation model with the warm dark matter and $Λ$CDM scenarios by studying CMB spectral distortions, halo abundances, and 21cm hydrogen lines.
We find constraints on inflationary dynamics that yield a large local bispectrum and/or trispectrum during two-field slow-roll inflation. This leads to simple relations between the non-Gaussianity parameters, simplifying the Suyama-Yamaguchi inequality and also producing a new result between the trispectrum parameters tNL and gNL.
In cosmological scenarios with thermal inflation, extra eras of moduli matter domination, thermal inflation and flaton matter domination exist between primordial inflation and the radiation domination of Big Bang nucleosynthesis. During these eras, cosmological perturbations on small scales can enter and re-exit the horizon, modifying the power spectrum on those scales. The largest modified scale, $k_\mathrm{b}$, touches the horizon size when the expansion changes from deflation to inflation at the transition from moduli domination to thermal inflation. We analytically calculate the evolution …
I construct a class of single small field models of inflation that can predict an observable gravitational wave signal in the cosmic microwave background anisotropoies, contrary to popular wisdom. The spectral index, its running, the tensor to scalar ratio and the number of e-folds can cover all the parameter space currently allowed by cosmological observations. A unique feature of models in this class is their ability to predict a negative spectral index running in accordance with recent cosmic microwave background observations. I comment on the new class of models from an effective field the…
Thermal inflation is a second epoch of exponential expansion at typical energy scales $V^{1/4} \sim 10^{6 \sim 8} \mathrm{GeV}$. If the usual primordial inflation is followed by thermal inflation, the primordial power spectrum is only modestly redshifted on large scales, but strongly suppressed on scales smaller than the horizon size at the beginning of thermal inflation, $k > k_{\rm b} = a_{\rm b} H_{\rm b}$. We calculate the spectral distortion of the cosmic microwave background generated by the dissipation of acoustic waves in this context. For $k_{\rm b} \ll 10^3 \mathrm{Mpc}^{-1}$, therma…
Modular inflation is the restriction to two fields of automorphic inflation, a general group based framework for multifield scalar field theories with curved target spaces, which can be parametrized by the comoving curvature perturbation ${\cal R}$ and the isocurvature perturbation tensor $S^{IJ}$. This paper describes the dynamics and observables of these perturbations and considers in some detail the special case of modular inflation as an extensive class of two-field inflation theories with a conformally flat target space. It is shown that the nonmodular nature of derivatives of modular for…
We make a more general determination of the inflationary observables in the standard 4-D and 5-D single-field inflationary scenarios, by the exact reconstruction of the dynamics of the inflation potential during the observable inflation with minimal number of assumptions: the computation does not assume the slow-roll approximation and is valid in all regimes if the field is monotonically rolling down its potential. Making use of the {\em Hamilton-Jacobi} formalism developed for the 5-D single-field inflation model,we compute the scale dependence of the amplitudes of the scalarand tensor pertur…
We study the impact of thermal inflation on the formation of cosmological structures and present astrophysical observables which can be used to constrain and possibly probe the thermal inflation scenario. These are dark matter halo abundance at high redshifts, satellite galaxy abundance in the Milky Way, and fluctuation in the 21-cm radiation background before the epoch of reionization. The thermal inflation scenario leaves a characteristic signature on the matter power spectrum by boosting the amplitude at a specific wavenumber determined by the number of e-foldings during thermal inflation (…
Thermal inflation models (which feature two inflationary stages) can display damped primordial curvature power spectra on small scales which generate damped matter fluctuations. For a reasonable choice of parameters, thermal inflation models naturally predict a suppression of the matter power spectrum on galactic and sub-galactic scales, mimicking the effect of warm or interacting dark matter. Matter power spectra in these models are also characterised by an excess of power (w.r.t. the standard $Λ$CDM power spectrum) just below the suppression scale. By running a suite of N-body simulations we…
We identify models of supersymmetric hybrid inflation in which the tensor-to-scalar ratio, a canonical measure of gravity waves produced during inflation, can be as large as 0.03 or so, which will be tested by the Planck satellite experiment. The scalar spectral index lies within the WMAP one sigma bounds, while $|d n_s / d\ln k| \lesssim 0.01$.
These lectures cover the theoretical structure and phenomenology of some basic mechanisms for inflation. A full treatment of the problem requires `ultraviolet completion' because of the sensitivity of inflation to quantum gravity effects, while the observables are elegantly parameterized using low energy field theory. String theory provides novel mechanisms for inflation, some subject to significant observational tests, with highly UV-sensitive tensor mode measurements being a prime example. Although the ultraviolet completion is not directly accessible experimentally, some of these mechanisms…
We consider Supersymmetric (SUSY) and non-SUSY models of chaotic inflation based on the simplest power-law potential with exponents n=2 and 4. We propose a convenient non-minimal coupling to gravity and a non-minimal kinetic term which ensure, mainly for n=4, inflationary observables favored by the BICEP2/Keck Array and Planck results. Inflation can be attained for subplanckian inflaton values with the corresponding effective theories retaining the perturbative unitarity up to the Planck scale.
Warm inflation is an inflationary scenario in which a thermal bath coexists with the inflaton during inflation. This is unlike standard cold inflation in which the Universe is effectively devoid of particles during inflation. The thermal bath in warm inflation is maintained by the dissipation of the inflaton's energy through its couplings to other fields. Many models of warm inflation have been proposed and their predictions have been compared with cosmological data. Certain models of inflation that are disallowed in the context of cold inflation by the data are allowed in the warm inflationar…
We investigate the primordial gravitational waves (PGWs) in the general scenario where the inflation is preceded by a pre-inflationary stage with the effective equation of state $w$. Comparing with the results in the usual inflationary models, the power spectrum of PGWs is modified in two aspects: One is the mixture of the perturbation modes caused by he presence of the pre-inflationary period, and the other is the thermal initial state formed at the Planck era of the early Universe. By investigating the observational imprints of these modifications on the B-mode polarization of cosmic microwa…
A model of high scale inflation is presented where the radial part of the Peccei-Quinn (PQ) field with a non-minimal coupling to gravity plays the role of the inflaton, and the QCD axion is the dark matter. A quantum fluctuation of $\mathcal{O}(H/2π)$ in the axion field will result in a smaller angular fluctuation if the PQ field is sitting at a larger radius during inflation than in the vacuum. This changes the effective axion decay constant, $f_a$, during inflation and dramatically reduces the production of isocurvature modes. This mechanism opens up a new window in parameter space where an …
We investigate supersymmetric hybrid inflation in a realistic model based on the gauge symmetry $SU(4)_c \times SU(2)_L \times SU(2)_R$. The minimal supersymmetric standard model (MSSM) $μ$ term arises, following Dvali, Lazarides, and Shafi, from the coupling of the MSSM electroweak doublets to a gauge singlet superfield which plays an essential role in inflation. The primordial monopoles are inflated away by arranging that the $SU(4)_c \times SU(2)_L \times SU(2)_R$ symmetry is broken along the inflationary trajectory. The interplay between the (above) $μ$ coupling, the gravitino mass, and th…
We consider a simplified version of supersymmetric smooth hybrid inflation which contains a single ultraviolet cutoff m_P = 2.4 x 10^{18} GeV, instead of the two cutoffs m_P and M_* ~ few x 10^{17} GeV that are normally employed. With global supersymmetry the scalar spectral index n_s ~ 0.97, which is in very good agreement with the WMAP observations. With a non-minimal Kahler potential, the supergravity version of the model is compatible with the current central values of n_s and also yields potentially observable gravity waves (tensor to scalar ratio r <~ 0.02).
We add a thermal noise to Starobinsky equation of slow roll inflation. We calculate the number of e-folds of the stochastic system. The power spectrum and the spectral index are evaluated from the fluctuations of e-folds using an expansion in the quantum and thermal noise terms.
The mechanism of thermal inflation, a relatively short period of accelerated expansion after primordial inflation, is a desirable ingredient for a certain class of particle physics models if they are not to be in contention with the cosmology of the early Universe. Though thermal inflation is most simply described in terms of a thermal effective potential, a thermal environment also gives rise to thermal fluctuations that must be taken into account. We numerically study the effects of these thermal fluctuations using lattice simulations. We conclude that though they do not ruin the thermal inf…
It is shown that a tensor-to-scalar ratio close to r = 0.03, which can be observed by Planck, is realized in supersymmetric hybrid inflation models with TeV-scale soft supersymmetry breaking terms. This extends our previous analysis, which also found r <~ 0.03 but employed intermediate scale soft terms. Other cosmological observables such as the scalar spectral index are in good agreement with the WMAP data.
We consider supersymmetric shifted hybrid inflation models with a red tilted scalar spectral index n_s in agreement with the WMAP 7-yr central value. If non-minimal supergravity corrections are included, these models can also support a tensor-to-scalar ratio as large as r = 0.02, which may be observable by the Planck Satellite. In contrast to the standard supersymmetric hybrid inflation scenario, topological defects produced via gauge symmetry breaking are inflated away in the shifted version of the theory.
Thermal inflation is an attractive solution to the cosmological moduli problem. However, domain walls may be formed after thermal inflation and some mechanisms are needed to eliminate the domain wall before it dominates the Universe. We point out that gravitational waves produced by the dynamics of domain walls may be observed by the pulsar timing experiments and future space-borne gravitational wave detectors, which provides a probe into the period of thermal inflation. We also show that the QCD instanton effect can effectively eliminate the domain walls with producing observable amount of gr…
We consider gravitational wave production during inflation in type IIB string theory, and the possibility of observable gravitational waves in small field inflation. We show that the gauge field excitations on a set of coincident D7 branes, itself critical for moduli stabilization and hence intrinsic to inflation in string theory, coupled with axion fields from bulk fluxes, can act as a spectator sector during inflation. This results in a large production of chiral gravitational waves, even for relatively small values of the axion-gauge field coupling. We extend this to include a monodromy for…
We describe how to apply the transport method to compute inflationary observables in a broad range of multiple-field models. The method is efficient and encompasses scenarios with curved field-space metrics, violations of slow-roll conditions and turns of the trajectory in field space. It can be used for an arbitrary mass spectrum, including massive modes and models with quasi-single-field dynamics. In this note we focus on practical issues. It is accompanied by a Mathematica code which can be used to explore suitable models, or as a basis for further development.
We describe the general inflationary dynamics that can arise with a single, canonically coupled field where the inflaton potential is a 4-th order polynomial. This scenario yields a wide range of combinations of the empirical spectral observables, $n_s$, $r$ and $α_s$. However, not all combinations are possible and next-generation cosmological experiments have the ability to rule out all inflationary scenarios based on this potential. Further, we construct inflationary priors for this potential based on physically motivated choices for its free parameters. These can be used to determine the de…
For a robust interpretation of upcoming observations from Planck and LHC experiments it is imperative to understand how the inflationary dynamics of a non-minimally coupled Higgs scalar field may affect the degeneracy of the inflationary observables. We constrain the inflationary observables and the Higgs boson mass during observable inflation by fitting the the Higgs inflationary potential directly to WMAP5+BAO+SN data. We obtain a Higgs mass a value of 143.73+14.97/-6.31 GeV at 95% CL for the central value of top quark mass. We also show that the inflation driven by a non-minimally coupled s…
Gravitational waves (GW) produced in the early Universe contribute to the number of relativistic degrees of freedom, $N_{\rm eff}$, during Big Bang Nucleosynthesis (BBN). By using the constraints on $N_{\rm eff}$, we present a new bound on how much the Universe could have expanded between horizon exit of the largest observable scales today and the end of inflation. We discuss the implications on inflationary models and show how the new constraints affect model selection. We also discuss the sensitivities of the current and planned GW observatories such as LIGO and LISA, and show that the const…
We calculate Large Scale Structure observables for non-Gaussianity arising from non-Bunch-Davies initial states in single field inflation. These scenarios can have substantial primordial non-Gaussianity from squeezed (but observable) momentum configurations. They generate a term in the halo bias that may be more strongly scale-dependent than the contribution from the local ansatz. We also discuss theoretical considerations required to generate an observable signature.
We consider primordial fluctuations in thermal inflation scenario. Since the thermal inflation drives about 10 $e$-folds after the standard inflation, the time of horizon-exit during inflation corresponding to the present observational scale shifts toward the end of inflation. It generally makes the primordial power spectrum more deviated from a scale-invariant one and hence renders some models inconsistent with observations. We present a mechanism of generating the primordial curvature perturbation at the end of thermal inflation utilizing a fluctuating coupling of a flaton field with the fie…
In this work, we revisit the non-minimally coupled Higgs Inflation scenario and investigate its observational viability in light of the current Cosmic Microwave Background, Baryon Acoustic Oscillation and type Ia Supernovae data. We explore the effects of the Coleman-Weinberg approximation to the Higgs potential in the primordial universe, connecting the predictions for the Lagrangian parameters at inflationary scales to the electroweak observables through Renormalization Group methods at two-loop order. As the main result, we find that observations on the electroweak scale are in disagreement…
We consider models of chaotic inflation driven by the real parts of a conjugate pair of Higgs superfields involved in the spontaneous breaking of a grand unification symmetry at a scale assuming its supersymmetric value. Employing quadratic Kaehler potentials with a prominent shift-symmetric part proportional to c- and a tiny violation, proportional to c+, included in a logarithm we show that the inflationary observables provide an excellent match to the recent Planck and Bicep2/Keck Array results setting, e.g., 0.012<=c+/c-<1/N where -N<0 is the prefactor of the logarithm. Moreover, we analyz…
We numerically generate the six-dimensional landscape of D3-brane inflation and identify patches of eternal inflation near sufficiently flat inflection points of the potential. We show that reasonable measures that select patches of eternal inflation in the landscape yield sharp predictions for the spectral properties of primordial perturbations on observable scales. These include a scalar tilt of .936, a running of the scalar tilt -.00103, undetectably small tensors and non-Gaussianity, and no observable spatial curvature. Our results explicitly demonstrate that precision cosmology probes the…
Using $δN$ formalism, in the context of a generic multi-field inflation driven on a non-flat field space background, we revisit the analytic expressions of the various cosmological observables such as scalar/tensor power spectra, scalar/tensor spectral tilts, non-Gaussianity parameters, tensor-to-scalar ratio, and the various runnings of these observables. In our backward formalism approach, the subsequent expressions of observables automatically include terms beyond the leading order slow-roll expansion correcting many of the expression at subleading order. To connect our analysis properly wi…
We revisit the framework of axion-like inflation in view of the possibility that the coupling of the inflaton to a non-Abelian topological charge density could lead to the generation of a rapidly thermalizing heat bath. Both dispersive (mass) and absorptive (friction) effects are included. For phenomenologically viable parameters, the system remains in a weak regime of warm inflation (thermal friction $\ll$ Hubble rate). For tensor perturbations we derive an interpolating formula that incorporates both vacuum and thermal production. The latter yields a model-independent frequency shape $\sim f…
When did the universe thermalize? In this talk I review the status of this issue and its importance in establishing the expected properties of dark matter, the growth of large-scale structure, and the viability of inflation models when confronted with CMB observations. I also present a novel approach to tackling the theoretical challenges surrounding inflationary (p)reheating, which seeks to extend past work on the Effective Field Theory of Inflation to the time of reheating.
Employing an effective field theory approach to inflationary perturbations, we analyze in detail the effect of curvature-generated Lagrangian operators on various observables, focusing on their running with scales. At quadratic order, we solve the equation of motion at next-to-leading leading order in a generalized slow-roll approximation for a very general theory of single-field inflation. We derive the resulting power spectrum, its tilt and running. We then focus on the contribution to the primordial non-Gaussianity amplitude f_{NL} sourced by a specific interaction term. We show that the ru…
We consider a class of models in which minimal gauged F-term hybrid inflation is coupled renormalisably to the minimal supersymmetric standard model (MSSM), with no extra ingredients; we call this class the "minimal hybrid inflationary supersymmetric standard model" (MHISSM). The singlet inflaton supplies the Higgs mu-term, and allows an exit from inflation to a vacuum characterised by large Higgs vevs. The true ground state is reached after an period of thermal inflation along the Higgs flat direction. The scalar spectral index is reduced from the standard F-term value, to approximately 0.976…
The simple $m^2ϕ^2$ potential as an inflationary model is coming under increasing tension with limits on the tensor-to-scalar ratio $r$ and measurements of the scalar spectral index $n_s$. Cubic Galileon interactions in the context of the Horndeski action can potentially reconcile the observables. However, we show that this cannot be achieved with only a constant Galileon mass scale because the interactions turn off too slowly, leading also to gradient instabilities after inflation ends. Allowing for a more rapid transition can reconcile the observables but moderately breaks the slow-roll appr…
A new model of thermal inflation is introduced, in which the mass of the thermal waterfall field is dependent on a light spectator scalar field. Using the $δN$ formalism, the "end of inflation" scenario is investigated in order to ascertain whether this model is able to produce the dominant contribution to the primordial curvature perturbation. A multitude of constrains are considered so as to explore the parameter space, with particular emphasis to key observational signatures. For natural values of the parameters, the model is found to yield a sharp prediction for the scalar spectral index a…
We point out the necessity of resolving the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We highlight the fact that this gauge dependence is due to the use of an asymmetric background current which is specific to a choice of coordinate system in the scalar manifold. Favoring simplicity over complexity, we further propose a practical shortcut to gauge-independent inflationary observables by using effective potential obtained from a polar-like background current choice. We demonstrate this shortcut for several explicit examples…
We construct a class of single small field models of inflation that can predict, contrary to popular wisdom, an observable gravitational wave signal in the cosmic microwave background anisotropies. The spectral index, its running, the tensor to scalar ratio and the number of e-folds can cover all the parameter space currently allowed by cosmological observations. A unique feature of models in this class is their ability to predict a negative spectral index running in accordance with recent cosmic microwave background observations. We discuss the new class of models from an effective field theo…
A safe way to reheat the universe, in models of natural and quadratic inflation, is through shift symmetric couplings between the inflaton $ϕ$ and the Standard Model (SM), since they do not generate loop corrections to the potential $V(ϕ)$. We consider such a coupling to SM gauge fields, of the form $ϕF\tilde{F}/f$, with sub-Planckian $f$. In this case gauge fields can be exponentially produced already {\it during inflation} and thermalize via interactions with charged particles, as pointed out in previous work. This can lead to a plasma of temperature $T$ during inflation and the thermal mass…
We study the effects of perturbative reheating on the evolution of the curvature perturbation ζ, in two-field inflation models. We use numerical methods to explore the sensitivity of f_NL, n_s and r to the reheating process, and present simple qualitative arguments to explain our results. In general, if a large non-Gaussian signal exists at the start of reheating, it will remain non zero at the end of reheating. Unless all isocurvature modes have completely decayed before the start of reheating, we find that the non-linearity parameter, f_NL, can be sensitive to the reheating timescale, and th…
We present a successful inflation model based on $λϕ^4$ potential in which a Standard Model (SM) singlet inflaton $ϕ$, with mass of around a TeV or less, also plays the role of a weakly interacting scalar dark matter particle (WIMP). The WIMP relic abundance generated after inflation is in accord with the current observations. The spectral index $n_s$ lies within the WMAP 1-$σ$ bounds, while the Planck satellite may observe the tensor-to-scalar ratio, a canonical measure of gravity waves, which we estimate lies between 0.003 and 0.007.An unbroken $Z_2$ parity ensures that the scalar WIMP is ab…
The recently proposed Trans-Planckian Censorship Conjecture (TCC) can be used to constrain the energy scale of inflation. The conclusions however depend on the assumptions about post-inflationary history of the Universe. E.g. in the standard case of a thermal post-inflationary history in which the Universe stays radiation dominated at all times from the end of inflation to the epoch of radiation matter equality, TCC has been used to argue that the Hubble parameter during inflation, $H_{\inf}$, is below ${\cal O}(0.1) ~{\rm GeV}$. Cosmological scenarios with a non-thermal post-inflationary hist…
We investigate non-thermal gravitino production after tribrid inflation in supergravity, which is a variant of supersymmetric hybrid inflation where three fields are involved in the inflationary model and where the inflaton field resides in the matter sector of the theory. In contrast to conventional supersymmetric hybrid inflation, where non-thermal gravitino production imposes severe constraints on the inflationary model, we find that the "non-thermal gravitino problem" is generically absent in models of tribrid inflation, mainly due to two effects: (i) With the inflaton in tribrid inflation…
Inflation provides a natural mechanism to account for the origin of cosmic structures. The generation of primordial inhomogeneities during inflation can be understood via the spontaneous creation of quanta from the vacuum. We show that when the corresponding {\it stimulated} creation of quanta is considered, the characteristics of the state of the universe at the onset of inflation are not diluted by the inflationary expansion and can be imprinted in the spectrum of primordial inhomogeneities. The non-gaussianities (particularly in the so-called squeezed configuration) in the cosmic microwave …
Heavy-ion colliders have revealed the process of "fast thermalization". This experimental breakthrough has led to new theoretical tools to study the thermalization process at both weak and strong coupling. We apply this to the reheating epoch of inflationary cosmology, and the formation of a cosmological quark gluon plasma (QGP). We compute the thermalization time of the QGP at reheating, and find it is determined by the energy scale of inflation and the shear viscosity to entropy ratio $η/s$; or equivalently, the tensor-to-scalar ratio and the strong coupling constant at the epoch of thermali…
We investigate the probability of obtaining an observable curvature perturbation, using as an example the minimal curvaton-higgs (MCH) model. We determine 'probably observable' and 'probably excluded' regions of parameter space assuming generic initial conditions and applying a stochastic approach for the curvaton's evolution during inflation. Inflation is assumed to last longer than the N_{obs} = 55 observable e-folds, and the total number of e-folds of inflation determines the particular ranges of parameters that are probable. For the MCH model, these 'probably observable' regions always lie…
We study a model of inflation with terms quadratic and logarithmic in the Ricci scalar, where the gravitational action is $f(R)=R+αR^2+βR^2 \ln R$. These terms are expected to arise from one loop corrections involving matter fields in curved space-time. The spectral index $n_s$ and the tensor to scalar ratio yield $10^{-4}\lesssim r\lesssim0.03$ and $0.94\lesssim n_s \lesssim 0.99$. i.e. $r$ is an order of magnitude bigger or smaller than the original Starobinsky model which predicted $r\sim 10^{-3}$. Further enhancement of $r$ gives a scale invariant $n_s\sim 1$ or higher. Other inflationary …
In some versions of the theory of inflation, it is assumed that before inflation began the universe was in a Friedmann-Robertson-Walker (FRW) stage, with the energy density dominated by massless particles. The origin of the nearly scale-invariant density perturbations is quantum fluctuations in the inflaton field. Here we point out that under those conditions there would necessarily also be large thermally induced density perturbations. It is asserted that inflation would smooth out any pre-existing perturbations. But that argument relies on linear perturbation theory of the scalar modes, whic…
We consider thermal, trapped and chromo-natural inflation in light of the swampland criteria and the Trans-Planckian Censorship Conjecture (TCC). Since thermal inflation occurs at energies low compared to those of Grand Unification, it is consistent with the TCC, and it is also consistent with the refined swampland conditions. Trapped and chromo-natural inflation are candidates for primordial (high energy scale) inflation. Since in both of these scenarios there are effective damping terms in the scalar field equation of motion, the models can easily be consistent with the swampland criteria. T…
