An Accelerating Universe without Lambda: Delta Gravity Using Monte Carlo

• Main Authors: Jorge Alfaro, Marco San Martín, Joaquín Sureda
• Format: Article
• Language: English
• Published: MDPI AG 2019-02-01
• Series: Universe
• Subjects: accelerated expansion; cosmological constant; cosmology; dark energy; Delta Gravity; modified gravity; phantom energy; supernovae
• Online Access: https://www.mdpi.com/2218-1997/5/2/51

A gravitational field model based on two symmetric tensors, <inline-formula> <math display="inline"> <semantics> <msub> <mi>g</mi> <mrow> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <msub> <mover accent="true"> <mi>g</mi> <mo stretchy="false">˜</mo> </mover> <mrow> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> </semantics> </math> </inline-formula>, is studied, using a Markov Chain Monte Carlo (MCMC) analysis with the most updated catalog of SN-Ia. In this model, new matter fields are added to the original matter fields, motivated by an additional symmetry (<inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi>δ</mi> <mo stretchy="false">˜</mo> </mover> </semantics> </math> </inline-formula> symmetry). We call them <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi>δ</mi> <mo stretchy="false">˜</mo> </mover> </semantics> </math> </inline-formula> matter fields. This theory predicts an accelerating Universe without the need to introduce a cosmological constant <inline-formula> <math display="inline"> <semantics> <mi mathvariant="sans-serif">Λ</mi> </semantics> </math> </inline-formula> by hand in the equations. We obtained a very good fit to the SN-Ia Data, and with this, we found the two free parameters of the theory called <i>C</i> and <inline-formula> <math display="inline"> <semantics> <msub> <mi>L</mi> <mn>2</mn> </msub> </semantics> </math> </inline-formula>. With these values, we have fixed all the degrees of freedom in the model. The last <inline-formula> <math display="inline"> <semantics> <msub> <mi>H</mi> <mn>0</mn> </msub> </semantics> </math> </inline-formula> local value measurement is in tension with the CMB Data from Planck. Based on an absolute magnitude <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>M</mi> <mi>V</mi> </msub> <mo>=</mo> <mo>−</mo> <mn>19.23</mn> </mrow> </semantics> </math> </inline-formula> for the SN, Delta Gravity finds <inline-formula> <math display="inline"> <semantics> <msub> <mi>H</mi> <mn>0</mn> </msub> </semantics> </math> </inline-formula> to be <inline-formula> <math display="inline"> <semantics> <mrow> <mn>74.47</mn> <mo>±</mo> <mn>1.63</mn> </mrow> </semantics> </math> </inline-formula> km/(s Mpc). This value is in concordance with the last measurement of the <inline-formula> <math display="inline"> <semantics> <msub> <mi>H</mi> <mn>0</mn> </msub> </semantics> </math> </inline-formula> local value, <inline-formula> <math display="inline"> <semantics> <mrow> <mn>73.83</mn> <mo>±</mo> <mn>1.48</mn> </mrow> </semantics> </math> </inline-formula> km/(s Mpc).