Chaotic inflation from nonlinear sigma models in supergravity

Abstract

Editor: J. HisanoWe present a common solution to the puzzles of the light Higgs or quark masses and the need for a shift symmetry and large field values in high scale chaotic inflation. One way to protect, for example, the Higgs from a large supersymmetric mass term is if it is the Nambu-Goldstone boson (NGB) of a nonlinear sigma model. However, it is well known that nonlinear sigma models (NLSMs) with nontrivial Kähler transformations are problematic to couple to supergravity. An additional field is necessary to make the Kähler potential of the NLSM invariant in supergravity. This field must have a shift symmetry -making it a candidate for the inflaton (or axion). We give an explicit example of such a model for the coset space SU(3)/SU(2) × U (1), with the Higgs as the NGB, including breaking the inflaton's shift symmetry and producing a chaotic inflation potential. This construction can also be applied to other models, such as one based on E 7 /SO(10) × U (1) × U (1) which incorporates the first two generations of (light) quarks as the Nambu-Goldstone multiplets, and has an axion in addition to the inflaton. Along the way we clarify and connect previous work on understanding NLSMs in supergravity and the origin of the extra field (which is the inflaton here), including a connection to Witten-Bagger quantization. This framework has wide applications to model building; a light particle from a NLSM requires, in supergravity, exactly the structure for chaotic inflaton or an axion.

Reconstructions of the dark-energy equation of state and the inflationary potential

“…(40) can be written in the form of (26) under the simple change of variable ω = 3 n 0 ln (ω). The same transformation can be applied in the master equation, (45), which is transformed into equation (40).…”

“…The same transformation can be applied in the master equation, (45), which is transformed into equation (40). Moreover, if we also apply the transformation (78) to (45), then the latter takes the form of the master equation, (26).…”

“…The differential equation, (26), was derived in [52] and it follows from the generalized Chaplygin gas [56] with λ = 2, that is for an EoS…”

“…Since they lead to different inflationary scenarios, particularly in respect of the density fluctuations produced, they have different observational consequences for the cosmic microwave background radiation, and this permits them to be finely constrained by observational data. Various inflaton potentials in general relativistic scalar field cosmology have been proposed in [5][6][7][8][9][10][11][12][13][14][15][16][17][18] , while for inflationary models in other gravity theories, where there are more possibilities, see [1,[19][20][21][22][23][24][25][26][27][28][29][30] and references therein.…”

Starobinsky-like inflation in no-scale supergravity Wess-Zumino model with Polonyi term

“…The first implementations of supersymmetric models of inflation considered only global SUSY. But since the dynamics of inflation occur at early stages of the history of the universe and is sensitive to UV scales, it is necessary to also consider local SUSY or supergravity (SUGRA) (for recent SUGRA inflation models see for example [23][24][25][26][27][28]). In SUGRA the so-called F -term scalar potential is sensitive to the shape of the Kähler potential, and this can lead to the re-emergence of the η-problem in the presence of quadratic contributions to the Kähler potential.…”