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Register a new userInfrared dynamics of a light scalar field in de Sitter
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Mehrdad Mirbabayi
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Inertial observers in de Sitter are surrounded by a horizon and see thermal fluctuations. To them, a massless scalar field appears to follow a random motion but any attractive potential, no matter how weak, will eventually stabilize the field. We study this thermalization process in the static patch (the spacetime region accessible to an individual observer) via a truncation to the low frequency spectrum. We focus on the distribution of the field averaged over a subhorizon region. At timescales much longer than the inverse temperature and to leading order in the coupling, we find the evolution to be Markovian, governed by the same Fokker-Planck equation that arises when the theory is studied in the inflationary setup.
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The long wavelength physics in a de Sitter region depends on the initial quantum state. While such long wavelength physics is under control for massive fields near the Hartle-Hawking vacuum state, such initial states make unnatural assumptions about initial data outside the region of causal contact of a local observer. We argue that a reasonable approximation to a maximum entropy state, one that makes minimal assumptions outside an observers horizon volume, is one where a cutoff is placed on a surface bounded by timelike geodesics, just outside the horizon. For sufficiently early times, such a cutoff induces secular logarithmic divergences with the expansion of the region. For massive fields, these effects sum to finite corrections at sufficiently late times. The difference between the cutoff correlators and Hartle-Hawking correlators provides a measure of the theoretical uncertainty due to lack of knowledge of the initial state in causally disconnected regions. These differences are negligible for primordial inflation, but can become significant during epochs with very long-lived de Sitter regions, such as we may be entering now.
We study the arguments given in [1] which suggest that the uplifting procedure in the KKLT construction is not valid. First we show that the modification of the SUSY breaking sector of the nilpotent superfield, as proposed in [1], is not consistent with non-linearly realized local supersymmetry of de Sitter supergravity. Keeping this issue aside, we also show that the corresponding bosonic potential does actually describe de Sitter uplifting.
Calculating the quantum evolution of a de Sitter universe on superhorizon scales is notoriously difficult. To address this challenge, we introduce the Soft de Sitter Effective Theory (SdSET). This framework holds for superhorizon modes whose comoving momentum is far below the UV scale, which is set by the inverse comoving horizon. The SdSET is formulated using the same approach that yields the Heavy Quark Effective Theory. The degrees of freedom that capture the long wavelength dynamics are identified with the growing and decaying solutions to the equations of motion. The operator expansion is organized using a power counting scheme, and loops can be regulated while respecting the low energy symmetries. For massive quantum fields in a fixed de Sitter background, power counting implies that all interactions beyond the horizon are irrelevant. Alternatively, if the fields are very light, the leading interactions are at most marginal, and resumming the associated logarithms using (dynamical) renormalization group techniques yields the evolution equation for canonical stochastic inflation. The SdSET is also applicable to models where gravity is dynamical, including inflation. In this case, diffeomorphism invariance ensures that all interactions are irrelevant, trivially implying the all-orders conservation of adiabatic density fluctuations and gravitational waves. We briefly touch on the application to slow-roll eternal inflation by identifying novel relevant operators. This work serves to demystify many aspects of perturbation theory outside the horizon, and has a variety of applications to problems of cosmological interest.
We consider phase transitions on (eternal) de Sitter in an O(N) symmetric scalar field theory. Making use of Starobinskys stochastic inflation we prove that deep infrared scalar modes cannot form a condensate -- and hence they see an effective potential that allows no phase transition. We show that by proving convexity of the effective potential that governs deep infrared field fluctuations both at the origin as well as at arbitrary values of the field. Next, we present numerical plots of the scalar field probability distribution function (PDF) and the corresponding effective potential for several values of the coupling constant at the asymptotic future timelike infinity of de Sitter. For small field values the effective potential has an approximately quadratic form, corresponding to a positive mass term, such that the corresponding PDF is approximately Gaussian. However, the curvature of the effective potential shows qualitatively different (typically much softer) behavior on the coupling constant than that implied by the Starobinsky-Yokoyama procedure. For large field values, the effective potential as expected reduces to the tree level potential plus a positive correction that only weakly (logarithmically) depends on the background field. Finally, we calculate the backreaction of fluctuations on the background geometry and show that it is positive.
In the setup of ghost condensation model the generalized second law of black hole thermodynamics can be respected under a radiatively stable assumption that couplings between the field responsible for ghost condensate and matter fields such as those in the Standard Model are suppressed by the Planck scale. Since not only black holes but also cosmology are expected to play important roles towards our better understanding of gravity, we consider a cosmological setup to test the theory of ghost condensation. In particular we shall show that the de Sitter entropy bound proposed by Arkani-Hamed, et.al. is satisfied if ghost inflation happened in the early epoch of our universe and if there remains a tiny positive cosmological constant in the future infinity. We then propose a notion of cosmological Page time after inflation.
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