The importance of GR’s principle of equivalence for kinematically determined Friedmann–Lemaître–Robertson–Walker universes

The Einstein equations and the Friedmann–Lemaître–Robertson–Walker (FLRW) metric are the foundation of modern cosmology. Whereas the geometric interpretation of the Einstein equations describes the action of gravity as the curvature of space by matter, the FLRW metric is built on Milne’s concept of a kinematically determined universe. Applying the FLRW metric to the Einstein equations yields the Friedmann equation which describes the expansion history of the universe in the reference frame of observers co-moving with the expansion, who, as a consequence of the equivalence principle, are free-falling, co-moving observers and perceive flat space in their local inertial frame. We use this fact to propose an extension to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow></mml:math> CDM, incorporating the initial conditions of the background universe, comprising the initial energy densities and the initial post-big bang expansion rate. The observed late-time accelerated expansion is then attributed to a kinematic effect akin to a dark energy (DE) component. Choosing the same <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ω</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>≃</mml:mo><mml:mn>0.3</mml:mn></mml:mrow></mml:math> as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow></mml:math> CDM, its equation of state parameter is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"><mml:mrow><mml:msub><mml:mrow><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub><mml:mo>≃</mml:mo><mml:mo>−</mml:mo><mml:mn>0.8</mml:mn></mml:mrow></mml:math> . The expansion history of this model displays the typical s-shape in the evolution of the scale factor, which is known from the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m5"><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow></mml:math> CDM concordance model.