Determining Evolution of Cosmological Constant, Gravitational Constant and Speed of Light Using Nonadiabatic Cosmological Model and LLR Findings
oleh: Rajendra P. Gupta
| Format: | Article |
|---|---|
| Diterbitkan: | MDPI AG 2019-06-01 |
Deskripsi
We have shown that the Hubble constant <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </semantics> </math> </inline-formula> embodies the information about the evolutionary nature of the cosmological constant <inline-formula> <math display="inline"> <semantics> <mi>Λ</mi> </semantics> </math> </inline-formula>, gravitational constant <inline-formula> <math display="inline"> <semantics> <mi>G</mi> </semantics> </math> </inline-formula>, and the speed of light <inline-formula> <math display="inline"> <semantics> <mi>c</mi> </semantics> </math> </inline-formula>. We have derived expressions for the time evolution of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>G</mi> <mo>/</mo> <msup> <mi>c</mi> <mn>2</mn> </msup> <mo> </mo> <mrow> <mo>(</mo> <mrow> <mo>≡</mo> <mi>K</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> and dark energy density <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>ε</mi> <mi>Λ</mi> </msub> </mrow> </semantics> </math> </inline-formula> related to <inline-formula> <math display="inline"> <semantics> <mi>Λ</mi> </semantics> </math> </inline-formula> by explicitly incorporating the nonadiabatic nature of the universe in the Friedmann equation. We have found <inline-formula> <math display="inline"> <semantics> <mrow> <mrow> <mo>(</mo> <mrow> <mi>d</mi> <mi>K</mi> <mo>/</mo> <mi>d</mi> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>/</mo> <mi>K</mi> <mo> </mo> <mo>=</mo> <mo> </mo> <mn>1.8</mn> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </semantics> </math> </inline-formula> and, for redshift <inline-formula> <math display="inline"> <semantics> <mi>z</mi> </semantics> </math> </inline-formula>,<inline-formula> <math display="inline"> <semantics> <mrow> <mo> </mo> <msub> <mi>ε</mi> <mrow> <mi>Λ</mi> <mo>,</mo> <mi>z</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>ε</mi> <mrow> <mi>Λ</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo> </mo> <mo>=</mo> <mo> </mo> <msup> <mrow> <mrow> <mo>[</mo> <mrow> <mn>0.4</mn> <mo>+</mo> <mn>0.6</mn> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mi>z</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mo>−</mo> <mn>1.5</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </semantics> </math> </inline-formula>. Since the two expressions are related, we believe that the time variation of <inline-formula> <math display="inline"> <semantics> <mi>K</mi> </semantics> </math> </inline-formula> (and therefore that of <inline-formula> <math display="inline"> <semantics> <mi>G</mi> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mi>c</mi> </semantics> </math> </inline-formula>) is manifested as dark energy in cosmological models. When we include the null finding of the lunar laser ranging (LLR) for <inline-formula> <math display="inline"> <semantics> <mrow> <mrow> <mo>(</mo> <mrow> <mi>d</mi> <mi>G</mi> <mo>/</mo> <mi>d</mi> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>/</mo> <mi>G</mi> </mrow> </semantics> </math> </inline-formula> and relax the constraint that <inline-formula> <math display="inline"> <semantics> <mi>c</mi> </semantics> </math> </inline-formula> is constant in LLR measurements, we get <inline-formula> <math display="inline"> <semantics> <mrow> <mrow> <mo>(</mo> <mrow> <mi>d</mi> <mi>G</mi> <mo>/</mo> <mi>d</mi> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>/</mo> <mi>G</mi> <mo> </mo> <mo>=</mo> <mo> </mo> <mn>5.4</mn> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mrow> <mo>(</mo> <mrow> <mi>d</mi> <mi>c</mi> <mo>/</mo> <mi>d</mi> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>/</mo> <mi>c</mi> <mo> </mo> <mo>=</mo> <mo> </mo> <mn>1.8</mn> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </semantics> </math> </inline-formula>. Further, when we adapt the standard <inline-formula> <math display="inline"> <semantics> <mi>Λ</mi> </semantics> </math> </inline-formula>CDM model for the <inline-formula> <math display="inline"> <semantics> <mi>z</mi> </semantics> </math> </inline-formula> dependency of <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>ε</mi> <mi>Λ</mi> </msub> </mrow> </semantics> </math> </inline-formula> rather than it being a constant, we obtain surprisingly good results fitting the SNe Ia redshift <inline-formula> <math display="inline"> <semantics> <mi>z</mi> </semantics> </math> </inline-formula> vs distance modulus <inline-formula> <math display="inline"> <semantics> <mo>µ</mo> </semantics> </math> </inline-formula> data. An even more significant finding is that the new <inline-formula> <math display="inline"> <semantics> <mi>Λ</mi> </semantics> </math> </inline-formula>CDM model, when parameterized with low redshift data set (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>z</mi> <mo> </mo> <mo><</mo> <mo> </mo> <mn>0.5</mn> </mrow> </semantics> </math> </inline-formula>), yields a significantly better fit to the data sets at high redshifts (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>z</mi> <mo> </mo> <mo>></mo> <mo> </mo> <mn>0.5</mn> </mrow> </semantics> </math> </inline-formula>) than the standard ΛCDM model. Thus, the new model may be considered robust and reliable enough for predicting distances of radiation emitting extragalactic redshift sources for which luminosity distance measurement may be difficult, unreliable, or no longer possible.