Constraining teleparallel gravity through Gaussian processes

Abstract

Abstract We apply Gaussian processes (GP) in order to impose constraints on teleparallel gravity and its f ( T ) extensions. We use available H ( z ) observations from (i) cosmic chronometers data (CC); (ii) Supernova type Ia (SN) data from the compressed pantheon release together with the CANDELS and CLASH multi-cycle treasury programs; and (iii) baryonic acoustic oscillation (BAO) datasets from the sloan digital sky survey. For the involved covariance functions, we consider four widely used choices, namely the square exponential, Cauchy, Matérn and rational quadratic kernels, which are consistent with one another within 1 σ confidence levels. Specifically, we use the GP approach to reconstruct a model-independent determination of the Hubble constant H 0 , for each of these kernels and dataset combinations. These analyses are complemented with three recently announced literature values of H 0 , namely (i) Riess <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">R</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>74.22</mml:mn> <mml:mo>±</mml:mo> <mml:mn>1.82</mml:mn> <mml:mspace class="nbsp" width="0.3333em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">k</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> <mml:mspace class="nbsp" width="0.3333em"/> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace class="nbsp" width="0.3333em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">M</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> ; (ii) H0LiCOW collaboration <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mtext>HW</mml:mtext> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>73</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.8</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.7</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace class="nbsp" width="0.3333em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">k</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> <mml:mspace class="nbsp" width="0.3333em"/> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace class="nbsp" width="0.3333em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">M</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> ; and (iii) Carnegie–Chicago Hubble programme <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mtext>TRGB</mml:mtext> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>69.8</mml:mn> <mml:mo>±</mml:mo> <mml:mn>1.9</mml:mn> <mml:mspace class="nbsp" width="0.3333em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">k</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> <mml:mspace class="nbsp" width="0.3333em"/> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace class="nbsp" width="0.3333em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">M</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> . Additionally, we investigate the transition redshift between the decelerating and accelerating cosmological phases through the GP reconstructed deceleration parameter. Furthermore, we reconstruct the model-independent evolution of the dark energy equation of state, and finally reconstruct the allowed f ( T ) functions. As a result, the ΛCDM model lies inside the allowed region at 1 σ in all the examined kernels and datasets, however a negative slope for f ( T ) versus T is slightly favoured.

Topics & Concepts