We study the power spectrum of super-Hubble fluctuations of an inflatonlike scalar field, the “system,” coupled to another scalar field, the “environment” during de Sitter inflation. We obtain the reduced density matrix for the inflaton fluctuations by integrating out the environmental degrees of freedom. These are considered to be massless and conformally coupled to gravity as a proxy to describe degrees of freedom that remain sub-Hubble all throughout inflation. The time evolution of the density matrix is described by a quantum master equation, which describes the decay of the vacuum state, the production of particles and correlated pairs and quantum entanglement between super and sub-Hubble degrees of freedom. The quantum master equation provides a nonperturbative resummation of secular terms from self-energy (loop) corrections to the inflaton fluctuations. In the case studied here these are Sudakov-type double logarithms which result in the decay of the power spectrum of inflaton fluctuations upon horizon crossing with a concomitant violation of scale invariance. The reduced density matrix and its quantum master equation furnish a powerful nonperturbative framework to study the effective field theory of long wavelength fluctuations by tracing short wavelength degrees of freedom.

We obtain the nonequilibrium effective action of an inflatonlike scalar field—the system—by tracing over sub-Hubble degrees of freedom of “environmental” light scalar fields. The effective action is stochastic leading to effective Langevin equations of motion for the fluctuations of the inflatonlike field, with self-energy corrections and stochastic noise correlators that obey a de Sitter space-time analog of a fluctuation dissipation relation. We solve the Langevin equation implementing a dynamical renormalization group resummation of the leading secular terms and obtain the corrections to the power spectrum of super-Hubble fluctuations of the inflaton field, $\mathcal{P}(k;\eta )={\mathcal{P}}_0(k)e^{-\gamma (k;\eta )}$ where ${\mathcal{P}}_0(k)$ is the nearly scale invariant power spectrum in absence of coupling. $\gamma (k;\eta )>0$ describes the suppression of the power spectrum; it features Sudakov-type double logarithms and entails violations of scale invariance. We also obtain the effective action for the case of a heavy scalar field of mass $M\gg H$; this case yields a local “Fermi” limit with a very weak self-interaction of the inflatonlike field and dissipative terms that are suppressed by powers of $H/M$. We conjecture on the possibility that the large scale anomalies in the cosmic microwave background may originate in dissipative processes from inflaton coupling to sub-Hubble degrees of freedom.

Mass bounds on dark matter (DM) candidates are obtained for particles that decouple in or out of equilibrium while ultrarelativistic with arbitrary isotropic and homogeneous distribution functions. A coarse grained Liouville invariant primordial phase-space density $\mathcal{D}$ is introduced which depends solely on the distribution function at decoupling. The density $\mathcal{D}$ is explicitly computed and combined with recent photometric and kinematic data on dwarf spheroidal satellite galaxies in the Milky Way (dShps) and the observed DM density today yielding upper and lower bounds on the mass, primordial phase-space densities, and velocity dispersion of the DM candidates. Combining these constraints with recent results from $N$-body simulations yields estimates for the mass of the DM particles in the range of a few keV. We establish in this way a direct connection between the microphysics of decoupling in or out of equilibrium and the constraints that the particles must fulfill to be suitable DM candidates. If chemical freeze-out occurs before thermal decoupling, light bosonic particles can Bose condense. We study such Bose-Einstein condensate (BEC) as a dark matter candidate. It is shown that, depending on the relation between the critical ($T_c$) and decoupling ($T_d$) temperatures, a BEC light relic could act as cold DM but the decoupling scale must be higher than the electroweak scale. The condensate hastens the onset of the nonrelativistic regime and tightens the upper bound on the particle’s mass. A nonequilibrium scenario which describes particle production and partial thermalization, sterile neutrinos produced out of equilibrium, and other DM models is analyzed in detail and the respective bounds on mass, primordial phase-space density, and velocity dispersion are obtained. Thermal relics with $m\sim \mathrm{\text{few}}\mathrm{keV}$ that decouple when ultrarelativistic and sterile neutrinos produced resonantly or nonresonantly lead to a primordial phase-space density compatible with cored dShps and disfavor cusped satellites. Light Bose-condensed DM candidates yield phase-space densities consistent with cores and if $T_c\gg T_d$ also with cusps. Phase-space density bounds on particles that decoupled nonrelativistically combined with recent results from $N$-body simulations suggest a potential tension for WIMPs with $m\sim 100\mathrm{GeV}$, $T_d\sim 10\mathrm{MeV}$.

We obtain the effective inflaton potential during slow-roll inflation by including the one-loop quantum corrections to the energy momentum tensor from scalar curvature and tensor perturbations as well as from light scalars and Dirac fermions coupled to the inflaton. During slow-roll inflation there is an unambiguous separation between super- and subhorizon contributions to the energy momentum tensor. The superhorizon part is determined by the curvature perturbations and scalar field fluctuations: both feature infrared enhancements as the inverse of a combination of slow-roll parameters which measure the departure from scale invariance in each case. Fermions and gravitons do not exhibit infrared divergences. The subhorizon part is completely specified by the trace anomaly of the fields with different spins and is solely determined by the space-time geometry. The one-loop corrections to the amplitude of curvature and tensor perturbations are obtained to leading order in slow roll and in the $(H/M_{\mathrm{Pl}}{)}^2$ expansion. A complete assessment of the backreaction problem up to one loop including bosons and fermions is provided. The result validates the effective field theory description of inflation and confirms the robustness of the inflationary paradigm to quantum fluctuations. Quantum corrections to the power spectra are expressed in terms of the CMB observables: $n_s$, $r$ and $d{n}_s/d\ln k$. Trace anomalies (especially the graviton part) dominate these quantum corrections in a definite direction: they enhance the scalar curvature fluctuations and reduce the tensor fluctuations.

The clustering properties of sterile neutrinos are studied within a simple extension of the minimal standard model, where these neutrinos are produced via the decay of a gauge singlet scalar. The distribution function after decoupling is strongly out of equilibrium and features an enhancement at small comoving momentum $\propto 1/\sqrt{p}$. Dark matter abundance and phase space density constraints from dwarf spheroidal galaxies constrain the mass in the keV range consistent with a Yukawa coupling to a gauge singlet with mass and vacuum expectation value in the range $\sim 100\mathrm{GeV}$ and a decoupling temperature of this order. The dark matter transfer function and power spectrum are obtained from the solution of the nonrelativistic Boltzmann-Vlasov equation in the matter dominated era. The small momentum enhancement of the nonequilibrium distribution function leads to long range memory of gravitational clustering and a substantial enhancement of the power spectrum at small scales as compared to a thermal relic or sterile neutrino produced via nonresonant mixing with active neutrinos. The scale of suppression of the power spectrum for a sterile neutrino with $m\sim \mathrm{keV}$ produced by scalar decay that decouples at $\sim 100\mathrm{GeV}$ is $\lambda \sim 488\mathrm{kpc}$. At large scales $T(k)\sim 1-C{k}^2/k_{\mathrm{fs}}^2(t_{\mathrm{eq}})+\cdots$ with $C\sim \mathrm{O}(1)$. At small scales $65\mathrm{kpc}\lesssim \lambda \lesssim 500\mathrm{kpc}$ corrections to the fluid description and memory of gravitational clustering become important, and we find $T(k)\simeq 1.902e^{-k/k_{\mathrm{fs}}(t_{\mathrm{eq}})}$, where $k_{\mathrm{fs}}(t_{\mathrm{eq}})\sim 0.013/\mathrm{kpc}$ is the free-streaming wave vector at matter-radiation equality. The enhancement of power at small scales may provide possible relief to the tension between the constraints from x-ray and Lyman-$\alpha$ forest data.

We investigate the relaxation and decay of a particle during inflation by implementing the dynamical renormalization group. This investigation allows us to give a meaningful definition for the decay rate in an expanding universe. As a prelude to a more general scenario, the method is applied here to study the decay of a particle in de Sitter inflation via a trilinear coupling to massless conformally coupled particles, both for wavelengths much larger and much smaller than the Hubble radius. For superhorizon modes we find that the decay is of the form ${\eta }^{{\Gamma }_1}$ with $\eta$ being conformal time and we give an explicit expression for ${\Gamma }_1$ to leading order in the coupling which has a noteworthy interpretation in terms of the Hawking temperature of de Sitter space-time. We show that if the mass $M$ of the decaying field is $\ll H$ then the decay rate during inflation is enhanced over the Minkowski space-time result by a factor $2H/\pi M$. For wavelengths much smaller than the Hubble radius we find that the decay law is $e$ with $C(\eta )$ the scale factor and $\alpha$ determined by the strength of the trilinear coupling. In all cases we find a substantial enhancement in the decay law as compared to Minkowski space-time. These results suggest potential implications for the spectrum of scalar density fluctuations as well as non-Gaussianities.