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Register a new userDynamical renormalization group methods in theory of eternal inflation
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Authors
Dmitry I. Podolsky
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Dynamics of eternal inflation on the landscape admits description in terms of the Martin-Siggia-Rose (MSR) effective field theory that is in one-to-one correspondence with vacuum dynamics equations. On those sectors of the landscape, where transport properties of the probability measure for eternal inflation are important, renormalization group fixed points of the MSR effective action determine late time behavior of the probability measure. I argue that these RG fixed points may be relevant for the solution of the gauge invariance problem for eternal inflation.
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The much-discussed swampland conjectures suggest significant constraints on the properties of string theory landscape and on the nature of the multiverse that this landscape can support. The conjectures are especially constraining for models of inflation; in particular, they exclude the existence of de Sitter (dS) vacua. If the conjectures are false and dS vacua do exist, it still appears that their construction in string theory requires a fair amount of fine-tuning, so they may be vastly outnumbered by AdS vacua. Here we explore the multiverse structure suggested by these considerations. We consider two scenarios: (i) a landscape where dS vacua are rare and (ii) a landscape where dS vacua do not exist and the dS potential maxima and saddle points are not flat enough to allow for the usual hilltop inflation, even though slow-roll inflation is possible on the slopes of the potential. We argue that in both scenarios inflation is eternal and all parts of the landscape that can support inflation get represented in the multiverse. The spacetime structure of the multiverse in such models is nontrivial and is rather different from the standard picture.
Eternal inflation requires upward fluctuations of the energy in a Hubble volume, which appear to violate the energy conditions. In particular, a scalar field in an inflating spacetime should obey the averaged null energy condition, which seems to rule out eternal inflation. Here we show how eternal inflation is possible when energy conditions (even the null energy condition) are obeyed. The critical point is that energy conditions restrict the evolution of any single quantum state, while the process of eternal inflation involves repeatedly selecting a subsector of the previous state, so there is no single state where the conditions are violated.
The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of quantum field models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameters values. The scalar electrodynamics inflationary scenario thus obtained are seen to be in good agreement with the most recent observational data.
We discuss the difference between various gauge-invariant quantities typically used in single-field inflation, namely synchronous $zeta_s$, comoving $zeta_c$, and unitary $zeta_u$ curvatures. We show that conservation of $zeta_c$ outside the horizon is quite restrictive on models as it leads to conservation of $zeta_s$ and $zeta_u$, whereas the reverse does not hold. We illustrate the consequence of these differences with two inflationary models: ultra-slow-roll (USR) and braiding-ultra-slow-roll (BUSR). In USR, we show that out of the three curvatures, only $zeta_s$ is conserved outside the horizon, and we connect this result to the concepts of separate universe and the usage of the $delta N$ formalism. We find that even though $zeta_s$ is conserved, there is still a mild violation of the separate universe approximation in the continuity equation. Nevertheless, the $delta N$ formalism can still be applied to calculate the primordial power spectrum of some gauge-invariant quantities such as $zeta_u$, although it breaks down for others such as the uniform-density curvature. In BUSR, we show that both $zeta_u$ and $zeta_s$ are conserved outside the horizon, but take different values. Additionally, since $zeta_u ot=zeta_c$ we find that the prediction for observable curvature fluctuations after inflation does not reflect $zeta_c$ at horizon crossing during inflation and moreover involves not just $zeta_u$ at that epoch but also the manner in which the braiding phase ends.
Eternal inflation, the idea that there is always a part of the universe that is expanding exponentially, is a frequent feature of inflationary models. It has been argued that eternal inflation requires the violation of energy conditions, creating doubts for the validity of such models. We show that eternal inflation is possible without any energy condition violation, highlighting the important role of decoherence and the selection of states in the inflationary process.
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