Unimodular Theory of Gravity in Light of the Latest Cosmological Data

The unimodular theory of gravity is an alternative perspective to the traditional general relativity of Einstein and opens new possibilities for exploring its implications in cosmology. In this paper, we investigated Unimodular Gravity (UG) with the cosmological data from the Pantheon sample of Type...

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Main Authors: Naveen K. Singh, Gopal Kashyap
Format: Article
Language:English
Published: MDPI AG 2023-10-01
Series:Universe
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Online Access:https://www.mdpi.com/2218-1997/9/11/469
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author Naveen K. Singh
Gopal Kashyap
author_facet Naveen K. Singh
Gopal Kashyap
author_sort Naveen K. Singh
collection DOAJ
description The unimodular theory of gravity is an alternative perspective to the traditional general relativity of Einstein and opens new possibilities for exploring its implications in cosmology. In this paper, we investigated Unimodular Gravity (UG) with the cosmological data from the Pantheon sample of Type Ia Supernovae (SNs) (2018), Baryon Acoustic Oscillations (BAOs), and the observational H(z) data from the Differential Age method (DA). We also used the Cosmic Microwave Background (CMB) distance priors from the Planck 2018 results. We considered a model consisting of a generalized cosmological constant, radiation, and a dark matter component along with normal matter. The considered theory respects only unimodular coordinate transformations. We first fit our model with low-redshift data from SNs and DA and determined the value of the model parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>ξ</mi><mo>,</mo><mspace width="0.166667em"></mspace><msub><mi>H</mi><mn>0</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula>. We found the best-fit value of parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ξ</mi><mo>=</mo><mn>6.03</mn><mo>±</mo><mn>0.40</mn></mrow></semantics></math></inline-formula>, which deviates slightly from 6, for which the theory becomes the standard general theory of relativity. We observed a small deviation in the value of the Hubble constant (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mn>0</mn></msub><mo>=</mo><mn>72.6</mn><mo>±</mo><mn>3.5</mn></mrow></semantics></math></inline-formula> km s<sup>−1</sup> Mpc<sup>−1</sup>) in the UG model compared with the standard <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM model (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mn>0</mn></msub><mo>=</mo><mn>72.2</mn><mo>±</mo><mn>1.2</mn></mrow></semantics></math></inline-formula> km s<sup>−1</sup> Mpc<sup>−1</sup>). Using the BAO + CMB constraint in the UG model, we obtained <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mn>0</mn></msub><mo>=</mo><mn>68.45</mn><mo>±</mo><mn>0.66</mn><mspace width="4pt"></mspace><mrow><mi>km</mi></mrow><mspace width="4pt"></mspace><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><msup><mrow><mi>Mpc</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ξ</mi></semantics></math></inline-formula> is ∼6.029. For the combined datasets (SN + DA + BAO + CMB), the estimated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mn>0</mn></msub><mo>=</mo><mn>69.01</mn><mo>±</mo><mn>0.60</mn><mspace width="4pt"></mspace><mrow><mi>km</mi></mrow><mspace width="4pt"></mspace><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mspace width="4pt"></mspace><msup><mrow><mi>Mpc</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ξ</mi><mo>∼</mo></mrow></semantics></math></inline-formula>6.037, and in standard gravity, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mn>0</mn></msub><mo>=</mo><mn>68.25</mn><mo>±</mo><mn>0.40</mn><mspace width="4pt"></mspace><mrow><mi>km</mi></mrow><mspace width="4pt"></mspace><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mspace width="4pt"></mspace><msup><mrow><mi>Mpc</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>.
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spelling doaj.art-a47f808889724bb1b8cf295c5daf7bf02023-11-24T15:09:48ZengMDPI AGUniverse2218-19972023-10-0191146910.3390/universe9110469Unimodular Theory of Gravity in Light of the Latest Cosmological DataNaveen K. Singh0Gopal Kashyap1Sir P.T. Sarvajanik College of Science, Surat 395001, Gujarat, IndiaDepartment of Physics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, IndiaThe unimodular theory of gravity is an alternative perspective to the traditional general relativity of Einstein and opens new possibilities for exploring its implications in cosmology. In this paper, we investigated Unimodular Gravity (UG) with the cosmological data from the Pantheon sample of Type Ia Supernovae (SNs) (2018), Baryon Acoustic Oscillations (BAOs), and the observational H(z) data from the Differential Age method (DA). We also used the Cosmic Microwave Background (CMB) distance priors from the Planck 2018 results. We considered a model consisting of a generalized cosmological constant, radiation, and a dark matter component along with normal matter. The considered theory respects only unimodular coordinate transformations. We first fit our model with low-redshift data from SNs and DA and determined the value of the model parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>ξ</mi><mo>,</mo><mspace width="0.166667em"></mspace><msub><mi>H</mi><mn>0</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula>. We found the best-fit value of parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ξ</mi><mo>=</mo><mn>6.03</mn><mo>±</mo><mn>0.40</mn></mrow></semantics></math></inline-formula>, which deviates slightly from 6, for which the theory becomes the standard general theory of relativity. We observed a small deviation in the value of the Hubble constant (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mn>0</mn></msub><mo>=</mo><mn>72.6</mn><mo>±</mo><mn>3.5</mn></mrow></semantics></math></inline-formula> km s<sup>−1</sup> Mpc<sup>−1</sup>) in the UG model compared with the standard <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM model (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mn>0</mn></msub><mo>=</mo><mn>72.2</mn><mo>±</mo><mn>1.2</mn></mrow></semantics></math></inline-formula> km s<sup>−1</sup> Mpc<sup>−1</sup>). Using the BAO + CMB constraint in the UG model, we obtained <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mn>0</mn></msub><mo>=</mo><mn>68.45</mn><mo>±</mo><mn>0.66</mn><mspace width="4pt"></mspace><mrow><mi>km</mi></mrow><mspace width="4pt"></mspace><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><msup><mrow><mi>Mpc</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ξ</mi></semantics></math></inline-formula> is ∼6.029. For the combined datasets (SN + DA + BAO + CMB), the estimated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mn>0</mn></msub><mo>=</mo><mn>69.01</mn><mo>±</mo><mn>0.60</mn><mspace width="4pt"></mspace><mrow><mi>km</mi></mrow><mspace width="4pt"></mspace><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mspace width="4pt"></mspace><msup><mrow><mi>Mpc</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ξ</mi><mo>∼</mo></mrow></semantics></math></inline-formula>6.037, and in standard gravity, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mn>0</mn></msub><mo>=</mo><mn>68.25</mn><mo>±</mo><mn>0.40</mn><mspace width="4pt"></mspace><mrow><mi>km</mi></mrow><mspace width="4pt"></mspace><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mspace width="4pt"></mspace><msup><mrow><mi>Mpc</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2218-1997/9/11/469unimodular gravitycosmological constantHubble parameterHubble tensiondark energy
spellingShingle Naveen K. Singh
Gopal Kashyap
Unimodular Theory of Gravity in Light of the Latest Cosmological Data
Universe
unimodular gravity
cosmological constant
Hubble parameter
Hubble tension
dark energy
title Unimodular Theory of Gravity in Light of the Latest Cosmological Data
title_full Unimodular Theory of Gravity in Light of the Latest Cosmological Data
title_fullStr Unimodular Theory of Gravity in Light of the Latest Cosmological Data
title_full_unstemmed Unimodular Theory of Gravity in Light of the Latest Cosmological Data
title_short Unimodular Theory of Gravity in Light of the Latest Cosmological Data
title_sort unimodular theory of gravity in light of the latest cosmological data
topic unimodular gravity
cosmological constant
Hubble parameter
Hubble tension
dark energy
url https://www.mdpi.com/2218-1997/9/11/469
work_keys_str_mv AT naveenksingh unimodulartheoryofgravityinlightofthelatestcosmologicaldata
AT gopalkashyap unimodulartheoryofgravityinlightofthelatestcosmologicaldata