A minimal set of invariants as a systematic approach to higher order gravity models: physical and cosmological constraints

Abstract

We compare higher order gravity models to observational constraints from magnitude-redshift supernova data, distance to the last scattering surface of the CMB, and Baryon Acoustic Oscillations. We follow a recently proposed systematic approach to higher order gravity models based on minimal sets of curvature invariants, and select models that pass some physical acceptability conditions (free of ghost instabilities, real and positive propagation speeds, and free of separatrices). Models that satisfy these physical and observational constraints are found in this analysis and do provide fits to the data that are very close to those of the LCDM concordance model. However, we find that the limitation of the models considered here comes from the presence of superluminal mode propagations for the constrained parameter space of the models.PACS numbers: 98.80.-k, 95.36.+x

Testing general relativity in cosmology

“…Now using the FLRW flat metric and a universe filled with matter and radiation, one derives the generalized Friedmann equation where and are the matter and radiation energy densities, respectively, a dot represents d / dt . Also, in terms of H , and Several models were proposed in De Felice and Tsujikawa ( 2009 ) and shown to be consistent with observations of supernova magnitude-redshift data, distance to the CMB surface, baryon acoustic oscillations (BAO), and Hubble Key project and age constraints in Moldenhauer and Ishak ( 2009 ) and Moldenhauer et al. ( 2010 ).…”

“…( 2006 ). Some models have been shown to be also free from other instabilities due to superluminal propagations and fit cosmological expansion constraints De Felice and Tsujikawa ( 2009 ), Moldenhauer and Ishak ( 2009 ) and Moldenhauer et al. ( 2010 ).…”

f(R) Theories

“…Hence the quantity characterizes the deviation of the background dynamics from the ΛCDM model. A number of authors studied cosmological dynamics for specific f ( R ) models [160, 382, 488, 252, 31, 198, 280, 72, 41, 159, 235, 1, 279, 483, 321, 432]. …”

Gamma-ray bursts and dark energy-dark matter interaction

“…One also considers the constraints from the effect of the baryon acoustic peak of the large‐scale correlation function at 100 h −1 Mpc separation detected by the SDSS luminous red galaxy sample (Moldenhauer & Ishak 2009; Reid et al 2010). The peak position is related to the quantity measured to be A 0 = 0.493, with an error of σ A = 0.017.…”

“…In this work, one considers models with interacting dark energy and dark matter components. There are several useful tools to probe the phenomenology of these models, such as cosmic microwave background radiation (CMBR) data (Komatsu et al 2010), baryon acoustic oscillation (BAO) (Moldenhauer & Ishak 2009; Reid et al 2010), Supernovae (SNe) data (Kessler et al 2009) and the deviation from the virial equilibrium of galaxy clusters (Bertolami, Gil Pedro & Le Delliou 2007, 2009; Abdalla 2009). It has been suggested (Schaefer 2003; Bertolami & Tavares 2006) that gamma‐ray burst (GRB) may be used to extend the Hubble diagram to high redshifts, greater than z = 5.…”