Ultralight dilaton oscillations and the cosmological constant

Abstract In this work, we present a model predicting the emergence of a cosmological constant from ultralight dilaton oscillations. We begin by introducing the gravitational action in the context of two-dimensional scalar-tensor gravity, where the action of the gravitational field with an arbitrary dilaton potential is derived. The equations of motion for the gravitational field are then formulated and solved. Finally, we propose a model where the energy of the oscillating dilaton particle-like leads to the appearance of a cosmological term in the metric. Our results indicate that the energy associated with the oscillations of a dilaton particle-like contributes to the emergence of a cosmological term in the Schwarzschild metric. This term is interpreted as a cosmological constant, suggesting that the oscillatory energy of the dilaton could be considered a potential candidate for explaining dark energy. Furthermore, we constrain the dilaton mass to be on the order of $$m_\varPhi \sim 10^{-13}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>Φ</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>13</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> eV/ $$c^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> , consistent with ultralight dark matter models.