Search for Screened Interactions Associated with Dark Energy below the100 μmLength Scale

Abstract

We present the results of a search for unknown interactions that couple to mass between an optically levitated microsphere and a gold-coated silicon cantilever. The scale and geometry of the apparatus enables a search for new forces that appear at distances below 100 µm and which would have evaded previous searches due to screening mechanisms. The data are consistent with electrostatic backgrounds and place upper limits on the strength of new interactions at < 0.1 fN in the geometry tested. For the specific example of a chameleon interaction with an inverse power law potential, these results exclude matter couplings β > 5.6 × 10 4 in the region of parameter space where the self-coupling Λ 5 meV and the microspheres are not fully screened.Observations indicate that the universe is expanding at an accelerating rate [1][2][3]. This acceleration can be explained by the presence of 'dark energy' throughout the universe [4]. Although the nature of dark energy is unknown, one possibility is that it consists of a scalar field that couples to mass [5,6]. Astrophysical measurements of the dark energy density imply an energy scale of Λ = 2.4 meV, corresponding to a length scale of c/Λ ∼ 80 µm.It might be possible to detect the presence of a scalar field constituting dark energy by searching for new interactions between objects separated by distances below the dark energy length scale [5][6][7][8]. In many cases, the resulting forces can be substantially larger than Newtonian gravity at short distances [6,9]. The most sensitive previous searches for violations of Newtonian gravity at or below the dark energy length scale employed macroscopic test masses or a conductive shield between the probe and test masses to minimize electromagnetic backgrounds [8,[10][11][12][13]. Although these experiments place stringent constraints on deviations from Newtonian gravity, it is possible to construct theories of dark energy involving new forces that could have avoided detection due to the geometry and scale of previous experiments [6,9,14,15]. For these screened interactions, recent searches using microscopic test masses such as atoms [16,17] or neutrons [18][19][20] often provide the strongest constraints.Several screening mechanisms have been proposed to evade existing experimental constraints on scalar interactions in the laboratory and solar system [6]. A specific example is the chameleon mechanism [21,22], in which the effective mass of the chameleon particle (corresponding to the inverse length scale of the interaction) depends on the local matter density. At cosmological distances where the matter density is low, the chameleon field would mediate a long range interaction that explains the accelerating expansion of the universe [23]. However, most laboratory experiments are carried out in regions of high matter density, where the forces arising from the chameleon interaction are suppressed. This work presents a search for screened interactions below the dark energy length scale using optically levitated µm-size dielectric spheres ...

Radiative Screening of Fifth Forces

“…Taking λ ∼ 10 −18 , v ∼ 10 3 TeV, and M ∼ 10 −5 M Pl , we can achieve α ∼ 1=100, l Comp ∼ 1 cm, and a strong firstorder phase transition with T c ∼ 1 MeV. This is particularly interesting, as a range of tabletop experiments are currently searching for screened fifth forces over ∼cm distance scales [5,[32][33][34][35][36][37][38] and pulsar timing arrays may be sensitive to the stochastic background of nHz gravitational waves from first-order phase transitions with critical temperatures in the MeV range [39]. For shorter Compton wavelengths, we can also obtain phase transitions at around the electroweak scale, potentially having gravitational-wave signatures in the mHz range of the forthcoming LISA satellite array [40].…”

“…(iii) In order to be in the symmetry-broken phase today, the cosmological density (ρ ¼ 3H 2 0 M 2 Pl ) must be below the degenerate point in Eq. (38),…”

Cavity optomechanical spectroscopy constraints chameleon dark energy scenarios

“…The black line indicates limits from neutron interferometry (indicated by shadows) [11]. The constraint of the levitated microsphere experiment [17] are denoted by the red line. Our results are about one or two orders of magnitude stronger than the ones from atom interferometry at the dark energy range can be measured down to a precision of the order of ∼ 10 −1 meV.…”

“…[17], the distinct difference of our scheme is focused on the quantum optomechanics detection using optical nonlinear spectrum. The chameleon induced coupling strength can be obtained from Eq.…”

“…These include torsion-balance experiments [7,8], gravity resonance spectroscopy [9,10]. Recent searches using microscopic test masses such as atom, neutron [11][12][13][14][15][16] and the levitated microspheres [17] often provide the strongest constraints.…”