COSMOS- \(e'\) -soft Higgsotic attractors
Eur. Phys. J. C
COSMOS-e -soft Higgsotic attractors
Sayantan Choudhury 0
0 Department of Theoretical Physics, Tata Institute of Fundamental Research , Colaba, Mumbai 400005 , India
In this work, we have developed an elegant algorithm to study the cosmological consequences from a huge class of quantum field theories (i.e. superstring theory, supergravity, extra dimensional theory, modified gravity, etc.), which are equivalently described by soft attractors in the effective field theory framework. In this description we have restricted our analysis for two scalar fields - dilaton and Higgsotic fields minimally coupled with Einstein gravity, which can be generalized for any arbitrary number of scalar field contents with generalized non-canonical and non-minimal interactions. We have explicitly used R2 gravity, from which we have studied the attractor and non-attractor phases by exactly computing two point, three point and four point correlation functions from scalar fluctuations using the InIn (Schwinger-Keldysh) and the δN formalisms. We have also presented theoretical bounds on the amplitude, tilt and running of the primordial power spectrum, various shapes (equilateral, squeezed, folded kite or counter-collinear) of the amplitude as obtained from three and four point scalar functions, which are consistent with observed data. Also the results from two point tensor fluctuations and the field excursion formula are explicitly presented for the attractor and non-attractor phase. Further, reheating constraints, scale dependent behavior of the couplings and the dynamical solution for the dilaton and Higgsotic fields are also presented. New sets of consistency relations between two, three and four point observables are also presented, which shows significant deviation from canonical slow-roll models. Additionally, three possible theoretical proposals have presented to overcome the tachyonic instability at the time of late time acceleration. Finally, we have also provided the bulk interpretation from the three and four point scalar correlation functions for completeness.
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S. Choudhury: Presently working as a Visiting (Post-Doctoral) fellow
at DTP, TIFR, Mumbai.
Contents
10.2 Dynamical dilaton at late times . . . . . . . . .
10.3 Details of the δN formalism . . . . . . . . . .
10.3.1 Useful field derivatives of N . . . . . .
10.3.2 Second-order perturbative solution with
various source . . . . . . . . . . . . . .
10.3.3 Expressions for perturbative solutions
in final hypersurface . . . . . . . . . . .
10.3.4 Shift in the inflaton field due to δN . . .
10.3.5 Various useful constants for δN . . . . .
10.4 Momentum dependent functions in four point
function . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction
The inflationary paradigm is a theoretical proposal which
attempts to solve various long-standing issues with standard
Big Bang cosmology and has been studied earlier in various
works [
1–12
]. But apart from the success of this theoretical
framework it is important to note that no single model exists
till now using which one can explain the complete evolution
history of the universe and also one is unable to break the
degeneracy between various cosmological parameters
computed from various models of inflation [
13–33
]. It is
important to note that we have the vacuum energy contribution
generated by the trapped Higgs field in a metastable vacuum
state which mimics the role of an effective cosmological
constant in effective theory. At the later stages of the universe
such a vacuum contribution dominates over other contents
and correspondingly the universe expands in an
exponential fashion. But using such metastable vacuum state it is
not possible to explain the tunneling phenomenon and also
impossible to explain the end of inflation. To serve both of the
purposes the effective potential for inflation should have a flat
structure. Due to such a specific structure the effective
potential for inflation satisfies the flatness or slow-roll condition
using which one can easily determine the field value
corresponding to the end of inflation. There are various classes
of models in existence in the cosmological literature where
one has derived such a specific structure of inflation [
14,34–
39
]. For example, the Coleman–Weinberg effective potential
serves this purpose [
40,41
]. Now if we consider the finite
temperature contributions in the effective potential [
42,43
]
then such thermal effects need to localize the inflaton field
to small expectation values at the beginning of inflation. The
flat structure of the effective potential for inflation is such
that the scalar inflaton field slowly rolls down in the valley of
potential during which the scale factor varies exponentially
and then inflation ends when the scalar inflaton field goes to
the non-slow-rolling region by violating the flatness
condition. At this epoch inflaton field evolve (...truncated)