Superpotential Method for Cosmological Models

—We construct the gravity models with exact particular solutions using the conformal transformation and the superpotential method for the corresponding models in the Einstein frame. The functions are obtained explicitly. We consider exact solutions for the obtained gravity model with the cosmological constant in detail.

[1]  S. Ketov On the equivalence of Starobinsky and Higgs inflationary models in gravity and supergravity , 2019, Journal of Physics A: Mathematical and Theoretical.

[2]  A. Dolgov,et al.  Instability Effects in F(R)-Modified Gravity and in Gravitational Baryogenesis , 2019, Physics of Particles and Nuclei.

[3]  M. Zubair,et al.  Dynamics of scalar potentials in theory of gravity , 2019, Canadian Journal of Physics.

[4]  Yohei Ema Dynamical emergence of scalaron in Higgs inflation , 2019, Journal of Cosmology and Astroparticle Physics.

[5]  M. Sami,et al.  Superpotential method for chiral cosmological models connected with modified gravity , 2019, Physical Review D.

[6]  A. Paliathanasis,et al.  Cosmological solutions in multiscalar field theory , 2019, The European Physical Journal C.

[7]  D. Gorbunov,et al.  Some like it hot: R2 heals Higgs inflation, but does not cool it , 2019, Physics Letters B.

[8]  A. Paliathanasis,et al.  Exact solutions in Chiral cosmology , 2018, General Relativity and Gravitation.

[9]  K. Tamvakis,et al.  Nonminimal Coleman-Weinberg inflation with an R2 term , 2018, Journal of Cosmology and Astroparticle Physics.

[10]  D. Gorbunov,et al.  Scalaron the healer: removing the strong-coupling in the Higgs- and Higgs-dilaton inflations , 2018, Physics Letters B.

[11]  J. Yokoyama,et al.  Inflation in the mixed Higgs-R2 model , 2018, Journal of Cosmology and Astroparticle Physics.

[12]  S. Capozziello,et al.  The role of energy conditions in f(R) cosmology , 2018, Physics Letters B.

[13]  J. Barrow,et al.  New integrable models and analytical solutions in f(R) cosmology with an ideal gas , 2018, 1801.01274.

[14]  G. Venturi,et al.  Integrable cosmological models in the Einstein and in the Jordan frames and Bianchi-I cosmology , 2016, Physics of Particles and Nuclei.

[15]  A. Ricciardone,et al.  Anisotropic cosmological solutions in R + R2 gravity , 2018 .

[16]  A. Paliathanasis Analytic solution of the Starobinsky model for inflation , 2017, 1706.06400.

[17]  Tower Wang,et al.  Primordial perturbations generated by Higgs field and $R^2$ operator , 2017, 1701.06636.

[18]  G. Venturi,et al.  General solutions of integrable cosmological models with non-minimal coupling , 2016, Physics of Particles and Nuclei Letters.

[19]  P. Binétruy,et al.  Universality in generalized models of inflation , 2016, 1611.07019.

[20]  G. Venturi,et al.  Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities , 2016, 1602.07192.

[21]  S. Ketov,et al.  Starobinsky-like two-field inflation , 2015, 1510.03524.

[22]  S. Ketov,et al.  The f(R) gravity function of the Linde quintessence , 2014, 1410.3557.

[23]  C. Rosset,et al.  Universality classes for models of inflation , 2014, 1407.0820.

[24]  V. Vennin Horizon-flow off-track for inflation , 2014, 1401.2926.

[25]  T. Harko,et al.  Arbitrary scalar-field and quintessence cosmological models , 2013, 1310.7167.

[26]  G. Venturi,et al.  Integrable cosmological models with non-minimally coupled scalar fields , 2013, 1312.3540.

[27]  A. Sorin,et al.  Integrable Scalar Cosmologies I. Foundations and links with String Theory , 2013, 1307.1910.

[28]  G. Venturi,et al.  Reconstruction of Scalar Potentials in Modified Gravity Models , 2012, 1211.6272.

[29]  A. Andrianov,et al.  General solution of scalar field cosmology with a (piecewise) exponential potential , 2011, 1105.4515.

[30]  Sergei D. Odintsov,et al.  Unified cosmic history in modified gravity: From F ( R ) theory to Lorentz non-invariant models , 2010, 1011.0544.

[31]  J. Yokoyama,et al.  Phantom Boundary Crossing and Anomalous Growth Index of Fluctuations in Viable f(R) Models of Cosmic Acceleration , 2010, 1002.1141.

[32]  Anjan A. Sen,et al.  Background cosmological dynamics in f(R) gravity and observational constraints , 2010, 1001.5384.

[33]  I. Aref’eva,et al.  Stable exact solutions in cosmological models with two scalar fields , 2009, 0911.5105.

[34]  T. Sotiriou,et al.  f(R) Theories Of Gravity , 2008, 0805.1726.

[35]  S. Nojiri,et al.  Crossing of the phantom divide in modified gravity , 2008, 0810.4296.

[36]  I. Fomin,et al.  On calculation of the cosmological parameters in exact models of inflation , 2008, 1704.05378.

[37]  E. Elizalde,et al.  Class of viable modified f(R) gravities describing inflation and the onset of accelerated expansion , 2007, 0712.4017.

[38]  A. Andrianov,et al.  Reconstruction of scalar potentials in two-field cosmological models , 2007, 0711.4300.

[39]  I. Aref’eva,et al.  Dynamics in nonlocal linear models in the Friedmann–Robertson–Walker metric , 2007, 0711.1364.

[40]  P. Townsend Hamilton–Jacobi mechanics from pseudo-supersymmetry , 2007, 0710.5178.

[41]  S. Tsujikawa Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints , 2007, 0709.1391.

[42]  A. Starobinsky Disappearing cosmological constant in f(R) gravity , 2007, 0706.2041.

[43]  Wayne Hu,et al.  Models of f(R) Cosmic Acceleration that Evade Solar-System Tests , 2007, 0705.1158.

[44]  Max Tegmark,et al.  Constraining f ( R ) gravity as a scalar-tensor theory , 2006, astro-ph/0612569.

[45]  D. Bazeia,et al.  First-order formalism for dust , 2006 .

[46]  D. Bazeia,et al.  First-order formalism and dark energy , 2005, astro-ph/0512197.

[47]  I. Aref’eva,et al.  Exactly Solvable SFT Inspired Phantom Model , 2004, astro-ph/0412619.

[48]  E. Elizalde,et al.  Late-time cosmology in (phantom) scalar-tensor theory: Dark energy and the cosmic speed-up , 2004, hep-th/0405034.

[49]  S. Nojiri,et al.  Modified gravity with negative and positive powers of the curvature: Unification of the inflation and of the cosmic acceleration , 2003, hep-th/0307288.

[50]  A. Dolgov,et al.  Can modified gravity explain accelerated cosmic expansion , 2003, astro-ph/0307285.

[51]  S. Capozziello,et al.  CURVATURE QUINTESSENCE MATCHED WITH OBSERVATIONAL DATA , 2003, astro-ph/0307018.

[52]  A. Starobinsky,et al.  Confrontation of a double inflationary cosmological model with observations , 1993, astro-ph/9309049.

[53]  Bond,et al.  Nonlinear evolution of long-wavelength metric fluctuations in inflationary models. , 1990, Physical review. D, Particles and fields.

[54]  A A Starobinsky,et al.  Power-law inflation as an attractor solution for inhomogeneous cosmological models , 1990 .

[55]  A G Muslimov On the scalar field dynamics in a spatially flat Friedman universe , 1990 .

[56]  K. Maeda,et al.  Towards the Einstein-Hilbert action via conformal transformation. , 1989, Physical review. D, Particles and fields.

[57]  Maeda Inflation as a transient attractor in R2 cosmology. , 1988, Physical review. D, Particles and fields.

[58]  Suen,et al.  The R2 cosmology: Inflation without a phase transition. , 1986, Physical review. D, Particles and fields.

[59]  A. Starobinsky,et al.  Dynamics of phase transition in the new inflationary universe scenario and generation of perturbations , 1982 .

[60]  A. Starobinsky,et al.  A new type of isotropic cosmological models without singularity , 1980 .

[61]  A. Ruzmaikin,et al.  Quadratic Corrections to the Lagrangian Density of the Gravitational Field and the Singularity , 1969 .