Anisotropic massive Brans–Dicke gravity extension of the standard $$\Lambda $$CDM model
Özgür Akarsu, Nihan Katırcı, Neşe Özdemir, J. Alberto Vázquez
Abstract
Abstract We present an explicit detailed theoretical and observational investigation of an anisotropic massive Brans–Dicke (BD) gravity extension of the standard $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> CDM model, wherein the extension is characterized by two additional degrees of freedom; the BD parameter, $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ω</mml:mi></mml:math> , and the present day density parameter corresponding to the shear scalar, $$\Omega _{\sigma ^2,0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>Ω</mml:mi><mml:mrow><mml:msup><mml:mi>σ</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math> . The BD parameter, determining the deviation from general relativity (GR), by alone characterizes both the dynamics of the effective dark energy (DE) and the redshift dependence of the shear scalar. These two affect each other depending on $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ω</mml:mi></mml:math> , namely, the shear scalar contributes to the dynamics of the effective DE, and its anisotropic stress – which does not exist in scalar field models of DE within GR – controls the dynamics of the shear scalar deviating from the usual $$\propto (1+z)^6$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>∝</mml:mo><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>6</mml:mn></mml:msup></mml:mrow></mml:math> form in GR. We mainly confine the current work to non-negative $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ω</mml:mi></mml:math> values as it is the right sign – theoretically and observationally – for investigating the model as a correction to the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> CDM. By considering the current cosmological observations, we find that $$\omega \gtrsim 250$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ω</mml:mi><mml:mo>≳</mml:mo><mml:mn>250</mml:mn></mml:mrow></mml:math> , $$\Omega _{\sigma ^2,0}\lesssim 10^{-23}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Ω</mml:mi><mml:mrow><mml:msup><mml:mi>σ</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>≲</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>23</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> and the contribution of the anisotropy of the effective DE to this value is insignificant. We conclude that the simplest anisotropic massive BD gravity extension of the standard $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> CDM model exhibits no significant deviations from it all the way to the Big Bang Nucleosynthesis. We also point out the interesting features of the model in the case of negative $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ω</mml:mi></mml:math> values; for instance, the constraints on $$\Omega _{\sigma ^2,0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>Ω</mml:mi><mml:mrow><mml:msup><mml:mi>σ</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math> could be relaxed considerably, the values of $$\omega \sim -1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ω</mml:mi><mml:mo>∼</mml:mo><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> (relevant to string theories) predict dramatically different dynamics for the expansion anisotropy.